Metamath Proof Explorer


Theorem nfaba1

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 14-Oct-2016) Add disjoint variable condition to avoid ax-13 . See nfaba1g for a less restrictive version requiring more axioms. (Revised by Gino Giotto, 20-Jan-2024)

Ref Expression
Assertion nfaba1
|- F/_ x { y | A. x ph }

Proof

Step Hyp Ref Expression
1 nfa1
 |-  F/ x A. x ph
2 1 nfab
 |-  F/_ x { y | A. x ph }