Theorem pimeq2d ≪ | index | src | ≫

theorem pimeq2d (G: wff) {x: nat} (p q1 q2: wff x):
  $ G -> (q1 <-> q2) $ >
  $ G -> ((P. x p -> q1) <-> (P. x p -> q2)) $;

Step	Hyp	Ref	Expression
1		pimeq2	A. x (q1 <-> q2) -> ((P. x p -> q1) <-> (P. x p -> q2))
2		hyp h1	G -> (q1 <-> q2)
3	2	iald	G -> A. x (q1 <-> q2)
4	1, 3	syl	G -> ((P. x p -> q1) <-> (P. x p -> q2))

Axiom use

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