Theorem pimeqd ≪ | index | src | ≫

theorem pimeqd (G: wff) {x: nat} (p1 p2 q1 q2: wff x):
  $ G -> (p1 <-> p2) $ >
  $ G -> (q1 <-> q2) $ >
  $ G -> ((P. x p1 -> q1) <-> (P. x p2 -> q2)) $;

Step	Hyp	Ref	Expression
1		hyp h1	G -> (p1 <-> p2)
2	1	pimeq1d	G -> ((P. x p1 -> q1) <-> (P. x p2 -> q1))
3		hyp h2	G -> (q1 <-> q2)
4	3	pimeq2d	G -> ((P. x p2 -> q1) <-> (P. x p2 -> q2))
5	2, 4	bitrd	G -> ((P. x p1 -> q1) <-> (P. x p2 -> q2))

Axiom use

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