Theorem sbeth ≪ | index | src | ≫

theorem sbeth (a: nat) (q: wff) {x: nat} (p: wff x):
  $ p $ >
  $ x = a -> (p <-> q) $ >
  $ q $;

Step	Hyp	Ref	Expression
1		hyp e	x = a -> (p <-> q)
2	1	sbe	[a / x] p <-> q
3		hyp h	p
4	3	sbth	[a / x] p
5	2, 4	mpbi	q

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp, itru), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12)