Metamath Proof Explorer


Theorem nfsabg

Description: Bound-variable hypothesis builder for a class abstraction. Usage of this theorem is discouraged because it depends on ax-13 . See nfsab for a version with more disjoint variable conditions, but not requiring ax-13 . (Contributed by Mario Carneiro, 11-Aug-2016) (New usage is discouraged.)

Ref Expression
Hypothesis nfsabg.1 x φ
Assertion nfsabg x z y | φ

Proof

Step Hyp Ref Expression
1 nfsabg.1 x φ
2 1 nf5ri φ x φ
3 2 hbabg z y | φ x z y | φ
4 3 nf5i x z y | φ