Theorem nfslem ≪ | index | src | ≫

theorem nfslem {x y: nat} (A: set y) (a: nat x) (B: set x):
  $ y = a -> A == B $ >
  $ FN/ x a $ >
  $ FS/ x B $;

Step	Hyp	Ref	Expression
1		eqscom	S[a / y] A == B -> B == S[a / y] A
2		hyp e	y = a -> A == B
3	2	sbse	S[a / y] A == B
4	1, 3	ax_mp	B == S[a / y] A
5		hyp h	FN/ x a
6		nfsv	FS/ x A
7	5, 6	nfsbsh	FS/ x S[a / y] A
8	4, 7	nfsx	FS/ x 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)