Theorem eqab2i ≪ | index | src | ≫

theorem eqab2i (A: set) {x: nat} (p: wff x):
  $ x e. A <-> p $ >
  $ A == {x | p} $;

Step	Hyp	Ref	Expression
1		hyp h	x e. A <-> p
2	1	a1i	T. -> (x e. A <-> p)
3	2	eqab2d	T. -> A == {x \| p}
4	3	trud	A == {x \| p}

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)