How do we prove the conclusion: ∀x(Ax ∨ ⇁Ax)
This is also called LEM, i.e. the Law of Excluded Middle. I'm confused while proving this because for ∀x, deduction assuming some constant is required. So, using universal quantifier Introduction and Elimination rules, how can the conclusion be reached?
Prove $(Aa \lor \neg Aa)$ from no premisses.
Then universally generalize. Which you can since $a$ appears in no live assumption.