Is the Law of Excluded Middle a valid deduction rule in court? If not, is it reasonable to say that all arguments in court must be "constructive in nature"?

As an example, consider this idealized and simplified scenario with the following facts:

1. If Alice's phone is not dead, she will see the news of Bob's death.
2. If Alice's phone is dead, she will ask Clare for a charger.
3. If Alice meets up with Clare, Clare will tell her about Bob's death.

Suppose I want to argue that Alice knows about Bob's death. Note that without knowing whether Alice's phone is dead or not, we can not constructively derive this fact. However if we assume the law of excluded middle, we can argue:

• If Alice's phone is not dead, by 1, our statement is true.
• If Alice's phone is dead, by 2 and 3, our statement is true.

My question is whether this kind of argument can be used in court, or that we must know whether Alice's phone is dead or not first concretely. Does the burden of proof change anything (i.e. whether this argument is made by the prosecutor or not)?