Theorem eleq2d ≪ | index | src | ≫

theorem eleq2d (G: wff) (a: nat) (A B: set):
  $ G -> A == B $ >
  $ G -> (a e. A <-> a e. B) $;

Step	Hyp	Ref	Expression
1		eleq2	A == B -> (a e. A <-> a e. B)
2		hyp h	G -> A == B
3	1, 2	syl	G -> (a e. A <-> a e. B)

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_12), axs_set (ax_8)