Theorem sbeq1d ≪ | index | src | ≫

theorem sbeq1d {x: nat} (G: wff x) (a b: nat x) (c: wff x):
  $ G -> a = b $ >
  $ G -> ([a / x] c <-> [b / x] c) $;

Step	Hyp	Ref	Expression
1		sbeq1	a = b -> ([a / x] c <-> [b / x] c)
2		hyp h	G -> a = b
3	1, 2	syl	G -> ([a / x] c <-> [b / x] c)

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)