Theorem abeqi ≪ | index | src | ≫

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

Step	Hyp	Ref	Expression
1		hyp h	p <-> q
2	1	a1i	T. -> (p <-> q)
3	2	abeqd	T. -> {x \| p} == {x \| q}
4	3	trud	{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)