Theorem nfab

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 nfabg for a less restrictive version requiring more axioms. (Revised by Gino Giotto, 20-Jan-2024)

	Ref	Expression
Hypothesis	nfab.1	$$⊢Ⅎx\phi$$
Assertion	nfab	$$⊢\underset{\_}{Ⅎ}x\left\{y|\phi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		nfab.1	$$⊢Ⅎx\phi$$
2	1	nfsab	$$⊢Ⅎxz\in \left\{y|\phi \right\}$$
3	2	nfci	$$⊢\underset{\_}{Ⅎ}x\left\{y|\phi \right\}$$