Theorem eleqd ≪ | index | src | ≫

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

Step	Hyp	Ref	Expression
1		hyp h1	G -> a = b
2	1	eleq1d	G -> (a e. A <-> b e. A)
3		hyp h2	G -> A == B
4	3	eleq2d	G -> (b e. A <-> b e. B)
5	2, 4	bitrd	G -> (a e. A <-> b 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)