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Metamath Proof Explorer

Theorem nfabg

Description: Bound-variable hypothesis builder for a class abstraction. Usage of this theorem is discouraged because it depends on ax-13 . See nfab 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 nfabg.1 
|- F/ x ph
Assertion nfabg 
|- F/_ x { y | ph }

Proof

Step Hyp Ref Expression
1 nfabg.1 
 |-  F/ x ph
2 1 nfsabg 
 |-  F/ x z e. { y | ph }
3 2 nfci 
 |-  F/_ x { y | ph }