Theorem eleq1d ≪ | index | src | ≫ 

theorem eleq1d (G: wff) (a b: nat) (A: set):
  $ G -> a = b $ >
  $ G -> (a e. A <-> b e. A) $;
StepHypRefExpression
1 eleq1 
a = b -> (a e. A <-> b e. A)
2 hyp h 
G -> a = b
3 1, 2 syl 
G -> (a e. A <-> b e. A)

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), axs_set (ax_8)