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	$$⊢Ⅎx\phi$$
Assertion	nfsab	$$⊢Ⅎxz\in \left\{y|\phi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		nfsab.1	$$⊢Ⅎx\phi$$
2	1	nf5ri	$$⊢\phi \to \forall x\phi$$
3	2	hbab	$$⊢z\in \left\{y|\phi \right\}\to \forall xz\in \left\{y|\phi \right\}$$
4	3	nf5i	$$⊢Ⅎxz\in \left\{y|\phi \right\}$$