Theorem eqab1d ≪ | index | src | ≫

theorem eqab1d (A: set) (G: wff) {x: nat} (p: wff x):
  $ G -> (p <-> x e. A) $ >
  $ G -> {x | p} == A $;

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