Theorem sbseqd ≪ | index | src | ≫

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

Step	Hyp	Ref	Expression
1		hyp h1	G -> a = b
2	1	sbseq1d	G -> S[a / x] A == S[b / x] A
3		hyp h2	G -> A == B
4	3	sbseq2d	G -> S[b / x] A == S[b / x] B
5	2, 4	eqstrd	G -> S[a / x] A == S[b / x] B

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, ax_8)