Theorem exbi ≪ | index | src | ≫

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

Step	Hyp	Ref	Expression
1		con1b	(~a <-> A. x ~a) -> (~A. x ~a <-> a)
2	1	conv ex	(~a <-> A. x ~a) -> (E. x a <-> a)
3		bicom	(A. x ~a <-> ~a) -> (~a <-> A. x ~a)
4		albi	A. x ~a <-> ~a
5	3, 4	ax_mp	~a <-> A. x ~a
6	2, 5	ax_mp	E. x a <-> a

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_12)