As a matter of fact, it turns out that this very question was more or less raised during the establishing of the Air Force. Browsing a reddit post churned out a nifty little document, hosted on justice.gov.

It is called 'MEMORANDUM FOR THE SPECIAL COUNSEL TO THE PRESIDENT', written by Harold I. Baynton, then Acting Assistant to the Attorney General, and written to, as per an editor's note,"Mr. Clark Clifford... It appears that Mr. Clifford was serving as Special Counsel to President Truman in 1947."

Within, he asserts that:

The phrase “Army and Navy” is used in the Constitution as a means of describing all the armed forces of the United States. The fact that one branch of the armed forces is called the “Air Force,” a name not known when the Constitution was adopted, and the fact that the Congress has seen fit to separate the air arm of our armed forces from the land and sea arms cannot detract from the President’s authority as Commander in Chief of all the armed forces.

and:

It certainly could not be contended that the absence of those words from the Constitution rendered the Congress unable to provide for an Air Force.

Though perhaps only an internal executive branch memo of some sort, it seems, it serves as an early source that serves to further bolster and back up the current and correct understanding as presented by the accepted answered.

As a matter of fact, it turns out that this very question was more or less raised during the establishing of the Air Force. Browsing a reddit post churned out a nifty little document, hosted on justice.gov.

It is called 'MEMORANDUM FOR THE SPECIAL COUNSEL TO THE PRESIDENT', written by Harold I. Baynton, then Acting Assistant to the Attorney General, and written to, as per an editor's note,"Mr. Clark Clifford... It appears that Mr. Clifford was serving as Special Counsel to President Truman in 1947."

Within, he asserts that:

The phrase “Army and Navy” is used in the Constitution as a means of describing all the armed forces of the United States. The fact that one branch of the armed forces is called the “Air Force,” a name not known when the Constitution was adopted, and the fact that the Congress has seen fit to separate the air arm of our armed forces from the land and sea arms cannot detract from the President’s authority as Commander in Chief of all the armed forces.

and:

It certainly could not be contended that the absence of those words from the Constitution rendered the Congress unable to provide for an Air Force.

Though perhaps only an internal executive branch memo of some sort, it seems, it serves as an early source that serves to further bolster and back up the current and correct understanding as presented by the accepted answered.

Another link brought up another interesting, albiet more modern, source. It's a 2005 website post by A. Michael Froomkin. Beyond the elobation on points already said here, he cites the case 'U.S. Air Force Board of Review in U.S. v. Naar, 951 WL 2298 (AFBR), 2 C.M.R. 739 (1952), wherein:

There, appellant, an Air Force officer, argued unsuccessfully that he had been prosecuted unlawfully because the Fifth Amendment states that “no person shall be held to answer for a capital or otherwise infamous crime, unless on a presentment of a Grand Jury, except in cases arising in the land or naval forces” and the Air Force was neither. The tribunal made short work of that argument.'

The point of sharing this specifically is to show our modern system has it nailed down. I can't find this case online, with this being the only source it seems, but I believe the author's credentials speak for themself.

As a matter of fact, it turns out that this very question was more or less raised during the establishing of the Air Force. Browsing a reddit post churned out a nifty little document, hosted on justice.gov.

It is called 'MEMORANDUM FOR THE SPECIAL COUNSEL TO THE PRESIDENT', written by Harold I. Baynton, then Acting Assistant to the Attorney General, and written to, as per an editor's note,"Mr. Clark Clifford... It appears that Mr. Clifford was serving as Special Counsel to President Truman in 1947."

Within, he asserts that:

The phrase “Army and Navy” is used in the Constitution as a means of describing all the armed forces of the United States. The fact that one branch of the armed forces is called the “Air Force,” a name not known when the Constitution was adopted, and the fact that the Congress has seen fit to separate the air arm of our armed forces from the land and sea arms cannot detract from the President’s authority as Commander in Chief of all the armed forces.

and:

It certainly could not be contended that the absence of those words from the Constitution rendered the Congress unable to provide for an Air Force.

Though perhaps only an internal executive branch memo of some sort, it seems, it serves as an early source that serves to further bolster sand back up the current and correct understanding as presented by the accepted answered.

As a matter of fact, it turns out that this very question was more or less raised during the establishing of the Air Force. Browsing a reddit post churned out a nifty little document, hosted on justice.gov.

It is called 'MEMORANDUM FOR THE SPECIAL COUNSEL TO THE PRESIDENT', written by Harold I. Baynton, then Acting Assistant to the Attorney General, and written to, as per an editor's note,"Mr. Clark Clifford... It appears that Mr. Clifford was serving as Special Counsel to President Truman in 1947."

Within, he asserts that:

The phrase “Army and Navy” is used in the Constitution as a means of describing all the armed forces of the United States. The fact that one branch of the armed forces is called the “Air Force,” a name not known when the Constitution was adopted, and the fact that the Congress has seen fit to separate the air arm of our armed forces from the land and sea arms cannot detract from the President’s authority as Commander in Chief of all the armed forces.

and:

It certainly could not be contended that the absence of those words from the Constitution rendered the Congress unable to provide for an Air Force.

Though perhaps only an internal executive branch memo of some sort, it seems, it serves as an early source that serves to further bolster and back up the current and correct understanding as presented by the accepted answered.