Theorem sbseq1d ≪ | index | src | ≫

theorem sbseq1d {x: nat} (G: wff) (a b: nat) (A: set x):
  $ G -> a = b $ >
  $ G -> S[a / x] A == S[b / x] A $;

Step	Hyp	Ref	Expression
1		hyp h	G -> a = b
2	1	sbeq1d	G -> ([a / x] y e. A <-> [b / x] y e. A)
3	2	abeqd	G -> {y \| [a / x] y e. A} == {y \| [b / x] y e. A}
4	3	conv sbs	G -> S[a / x] A == S[b / x] A

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp, itru), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12), axs_set (elab)