Theorem sbsed ≪ | index | src | ≫

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

Step	Hyp	Ref	Expression
1		sbset	A. x (x = a -> A == B) -> S[a / x] A == B
2		hyp e	G /\ x = a -> A == B
3	2	ialda	G -> A. x (x = a -> A == B)
4	1, 3	syl	G -> S[a / x] A == 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)