Theorem eleq2d | index | src |

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