Theorem pimim2d ≪ | index | src | ≫

theorem pimim2d (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		pimim2	A. x (q1 -> q2) -> (P. x p -> q1) -> (P. x p -> q2)
2		hyp h	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)