Theorem pimeq1d ≪ | index | src | ≫

theorem pimeq1d (G: wff) {x: nat} (p1 p2 q: wff x):
  $ G -> (p1 <-> p2) $ >
  $ G -> ((P. x p1 -> q) <-> (P. x p2 -> q)) $;

Step	Hyp	Ref	Expression
1		pimeq1	A. x (p1 <-> p2) -> ((P. x p1 -> q) <-> (P. x p2 -> q))
2		hyp h1	G -> (p1 <-> p2)
3	2	iald	G -> A. x (p1 <-> p2)
4	1, 3	syl	G -> ((P. x p1 -> q) <-> (P. x p2 -> q))

Axiom use

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