Theorem nfnlem ≪ | index | src | ≫

theorem nfnlem {x y: nat} (b: nat y) (a c: nat x):
  $ y = a -> b = c $ >
  $ FN/ x a $ >
  $ FN/ x c $;

Step	Hyp	Ref	Expression
1		eqcom	N[a / y] b = c -> c = N[a / y] b
2		hyp e	y = a -> b = c
3	2	sbne	N[a / y] b = c
4	1, 3	ax_mp	c = N[a / y] b
5		hyp h	FN/ x a
6		nfnv	FN/ x b
7	5, 6	nfsbnh	FN/ x N[a / y] b
8	4, 7	nfnx	FN/ x 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, the0)