Theorem nfsbsh ≪ | index | src | ≫

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

Step	Hyp	Ref	Expression
1		elsbs	z e. S[a / y] A <-> [a / y] z e. A
2		hyp h1	FN/ x a
3		hyp h2	FS/ x A
4	3	nfel2	F/ x z e. A
5	2, 4	nfsbh	F/ x [a / y] z e. A
6	1, 5	nfx	F/ x z e. S[a / y] A
7	6	nfsri	FS/ x S[a / y] 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)