Theorem nfsab1

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by Mario Carneiro, 11-Aug-2016) Remove use of ax-12 . (Revised by SN, 20-Sep-2023)

	Ref	Expression
Assertion	nfsab1	$$⊢Ⅎxy\in \left\{x|\phi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		df-clab	$$⊢y\in \left\{x|\phi \right\}\leftrightarrow \left[y/x\right]\phi$$
2		nfs1v	$$⊢Ⅎx\left[y/x\right]\phi$$
3	1 2	nfxfr	$$⊢Ⅎxy\in \left\{x|\phi \right\}$$