Theorem sbned ≪ | index | src | ≫

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

Step	Hyp	Ref	Expression
1		sbnet	A. x (x = a -> b = c) -> N[a / x] b = c
2		hyp e	G /\ x = a -> b = c
3	2	ialda	G -> A. x (x = a -> b = c)
4	1, 3	syl	G -> N[a / x] b = c

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), axs_the (theid)