Theorem nfsab

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016) Add disjoint variable condition to avoid ax-13 . See nfsabg for a less restrictive version requiring more axioms. (Revised by Gino Giotto, 20-Jan-2024)

	Ref	Expression
Hypothesis	nfsab.1	|- F/ x ph
Assertion	nfsab	|- F/ x z e. { y | ph }

Proof

Step	Hyp	Ref	Expression
1		nfsab.1	|- F/ x ph
2	1	nf5ri	|- ( ph -> A. x ph )
3	2	hbab	|- ( z e. { y | ph } -> A. x z e. { y | ph } )
4	3	nf5i	|- F/ x z e. { y | ph }