Theorem pimeqe ≪ | index | src | ≫

theorem pimeqe {x: nat} (a: nat) (p: wff x) (q: wff):
  $ x = a -> (p <-> q) $ >
  $ (P. x x = a -> p) <-> q $;

Step	Hyp	Ref	Expression
1		hyp e	x = a -> (p <-> q)
2	1	anwr	T. /\ x = a -> (p <-> q)
3	2	pimeqed	T. -> ((P. x x = a -> p) <-> q)
4	3	trud	(P. x x = a -> p) <-> q

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp, itru), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12)