Theorem nfsabg

Description: Bound-variable hypothesis builder for a class abstraction. Usage of this theorem is discouraged because it depends on ax-13 . See nfsab for a version with more disjoint variable conditions, but not requiring ax-13 . (Contributed by Mario Carneiro, 11-Aug-2016) (New usage is discouraged.)

	Ref	Expression
Hypothesis	nfsabg.1	$$⊢Ⅎx\phi$$
Assertion	nfsabg	$$⊢Ⅎxz\in \left\{y|\phi \right\}$$

Proof

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