Theorem nfs1

Description: If y is not free in ph , x is not free in [ y / x ] ph . Usage of this theorem is discouraged because it depends on ax-13 . Check out nfs1v for a version requiring less axioms. (Contributed by Mario Carneiro, 11-Aug-2016) (New usage is discouraged.)

	Ref	Expression
Hypothesis	nfs1.1	$$⊢Ⅎy\phi$$
Assertion	nfs1	$$⊢Ⅎx\left[y/x\right]\phi$$

Proof

Step	Hyp	Ref	Expression
1		nfs1.1	$$⊢Ⅎy\phi$$
2	1	nf5ri	$$⊢\phi \to \forall y\phi$$
3	2	hbsb3	$$⊢\left[y/x\right]\phi \to \forall x\left[y/x\right]\phi$$
4	3	nf5i	$$⊢Ⅎx\left[y/x\right]\phi$$