Metamath Proof Explorer


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 fewer axioms. (Contributed by Mario Carneiro, 11-Aug-2016) (New usage is discouraged.)

Ref Expression
Hypothesis nfs1.1 y φ
Assertion nfs1 x y x φ

Proof

Step Hyp Ref Expression
1 nfs1.1 y φ
2 1 nf5ri φ y φ
3 2 hbsb3 y x φ x y x φ
4 3 nf5i x y x φ