Theorem alex ≪ | index | src | ≫

theorem alex {x: nat} (a: wff x): $ A. x a <-> ~E. x ~a $;

Step	Hyp	Ref	Expression
1		bitr	(A. x a <-> A. x ~~a) -> (A. x ~~a <-> ~E. x ~a) -> (A. x a <-> ~E. x ~a)
2		notnot	a <-> ~~a
3	2	aleqi	A. x a <-> A. x ~~a
4	1, 3	ax_mp	(A. x ~~a <-> ~E. x ~a) -> (A. x a <-> ~E. x ~a)
5		alnex	A. x ~~a <-> ~E. x ~a
6	4, 5	ax_mp	A. x a <-> ~E. x ~a

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4)