Theorem sbneh ≪ | index | src | ≫

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

Step	Hyp	Ref	Expression
1		hyp h	FN/ x c
2	1	sbneht	A. x (x = a -> b = c) -> N[a / x] b = c
3		hyp e	x = a -> b = c
4	3	ax_gen	A. x (x = a -> b = c)
5	2, 4	ax_mp	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)