Theorem abeqd ≪ | index | src | ≫

theorem abeqd (G: wff) {x: nat} (p q: wff x):
  $ G -> (p <-> q) $ >
  $ G -> {x | p} == {x | q} $;

Step	Hyp	Ref	Expression
1		abeq	A. x (p <-> q) -> {x \| p} == {x \| q}
2		hyp h	G -> (p <-> q)
3	2	iald	G -> A. x (p <-> q)
4	1, 3	syl	G -> {x \| p} == {x \| 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), axs_set (elab)