Theorem nfsbs1h ≪ | index | src | ≫

theorem nfsbs1h {x: nat} (a: nat x) (A: set x):
  $ FN/ x a $ >
  $ FS/ x S[a / x] A $;

Step	Hyp	Ref	Expression
1		elsbs	y e. S[a / x] A <-> [a / x] y e. A
2		hyp h	FN/ x a
3	2	nfsb1h	F/ x [a / x] y e. A
4	1, 3	nfx	F/ x y e. S[a / x] A
5	4	nfsri	FS/ x S[a / x] A

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)