Theorem eqeqd ≪ | index | src | ≫

theorem eqeqd (G: wff) (a b c d: nat):
  $ G -> a = b $ >
  $ G -> c = d $ >
  $ G -> (a = c <-> b = d) $;

Step	Hyp	Ref	Expression
1		hyp h1	G -> a = b
2	1	eqeq1d	G -> (a = c <-> b = c)
3		hyp h2	G -> c = d
4	3	eqeq2d	G -> (b = c <-> b = d)
5	2, 4	bitrd	G -> (a = c <-> b = d)

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)