Solve this problem by using Hilbert style proof:
$ A,B \vdash A \equiv B $
my try :
- (1) A (hyp)
- (2) B (hyp)
- (3) $ A \land B $ (merge)
- (4) $ A \land B \equiv A \equiv B \equiv A \lor B $ (golden rule)
- (5) $ A \equiv B \equiv A \lor B $ (3,4 + equ)
- (6) $ A \lor B \equiv A \equiv B $ (Symmetry)
That was my try. I don't know if it was right. I couldn't continue.
Inference rules : leibniz and equanimity.
Lists of axioms and theorems :