Theorem nfsbnh ≪ | index | src | ≫

theorem nfsbnh {x y: nat} (a b: nat x y):
  $ FN/ x a $ >
  $ FN/ x b $ >
  $ FN/ x N[a / y] b $;

Step	Hyp	Ref	Expression
1		hyp h1	FN/ x a
2		hyp h2	FN/ x b
3	2	nfeq2	F/ x z = b
4	1, 3	nfsbh	F/ x [a / y] z = b
5	4	nfab	FS/ x {z \| [a / y] z = b}
6	5	nfthe	FN/ x the {z \| [a / y] z = b}
7	6	conv sbn	FN/ x N[a / y] 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), axs_the (theid, the0)