Theorem sbne ≪ | index | src | ≫

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

Step	Hyp	Ref	Expression
1		nfnv	FN/ x c
2		hyp e	x = a -> b = c
3	1, 2	sbneh	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)