Metamath Proof Explorer


Theorem nfsab1

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016) Remove use of ax-12 . (Revised by SN, 20-Sep-2023)

Ref Expression
Assertion nfsab1
|- F/ x y e. { x | ph }

Proof

Step Hyp Ref Expression
1 df-clab
 |-  ( y e. { x | ph } <-> [ y / x ] ph )
2 nfs1v
 |-  F/ x [ y / x ] ph
3 1 2 nfxfr
 |-  F/ x y e. { x | ph }