Theorem iex ≪ | index | src | ≫

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

Step	Hyp	Ref	Expression
1		eqcom	y = x -> x = y
2		ax_6	E. x x = y
3		exim	A. x (x = y -> a) -> E. x x = y -> E. x a
4	2, 3	mpi	A. x (x = y -> a) -> E. x a
5		ax_12	x = y -> a -> A. x (x = y -> a)
6	4, 5	syl6	x = y -> a -> E. x a
7	1, 6	rsyl	y = x -> a -> E. x a
8	7	eex	E. y y = x -> a -> E. x a
9		ax_6	E. y y = x
10	8, 9	ax_mp	a -> E. x 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)