Theorem hbab1

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by NM, 26-May-1993) (Proof shortened by Wolf Lammen, 25-Oct-2024)

	Ref	Expression
Assertion	hbab1	$$⊢y\in \left\{x|\phi \right\}\to \forall xy\in \left\{x|\phi \right\}$$

Proof

Step	Hyp	Ref	Expression
1		nfsab1	$$⊢Ⅎxy\in \left\{x|\phi \right\}$$
2	1	nf5ri	$$⊢y\in \left\{x|\phi \right\}\to \forall xy\in \left\{x|\phi \right\}$$