Theorem sbethh ≪ | index | src | ≫

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

Step	Hyp	Ref	Expression
1		hyp h	F/ x q
2		hyp e	x = a -> (p <-> q)
3	1, 2	sbeh	[a / x] p <-> q
4		hyp hp	p
5	4	sbth	[a / x] p
6	3, 5	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)