I have been trying to become more rigorous in general, and have been trying to practice with elementary set theory. I came across the idea of existential instantiation, in which we can suppose we have an arbitrary object which satisfies a particular property. In relation to set theory, I believe this means if we have a set $A$ and know $A$ is not the empty set, then we can use existential instantiation to suppose there exists $a \in A$. My question is, is there a limit to the number of times we may apply existential instantiation? For instance, if $A = \{1\}$, may I use existential instantiation more than once despite knowing that only one object exists in A? In other words, I may suppose $a, b, c \in A$ even though all three of them will be the same object? I believe the answer is there is no limit to the number of times I may apply existential instantiation, but would like some guidance confirming my opinion since I am self-studying.
Thank you for taking the time to help a novice!
