Theorem eqab1i ≪ | index | src | ≫

theorem eqab1i (A: set) {x: nat} (p: wff x):
  $ p <-> x e. A $ >
  $ {x | p} == A $;

Step	Hyp	Ref	Expression
1		hyp h	p <-> x e. A
2	1	a1i	T. -> (p <-> x e. A)
3	2	eqab1d	T. -> {x \| p} == A
4	3	trud	{x \| p} == A

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, ax_8)