Theorem aleqdh ≪ | index | src | ≫

theorem aleqdh {x: nat} (G a b: wff x):
  $ F/ x G $ >
  $ G -> (a <-> b) $ >
  $ G -> (A. x a <-> A. x b) $;

Step	Hyp	Ref	Expression
1		aleq	A. x (a <-> b) -> (A. x a <-> A. x b)
2		hyp h1	F/ x G
3		hyp h	G -> (a <-> b)
4	2, 3	ialdh	G -> A. x (a <-> b)
5	1, 4	syl	G -> (A. x a <-> A. x b)

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)