Theorem hbab1

Description: Bound-variable hypothesis builder for a class abstraction. (Contributed by NM, 26-May-1993)

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

Proof

Step	Hyp	Ref	Expression
1		df-clab	$$⊢y\in \left\{x|\phi \right\}\leftrightarrow \left[y/x\right]\phi$$
2		hbs1	$$⊢\left[y/x\right]\phi \to \forall x\left[y/x\right]\phi$$
3	1 2	hbxfrbi	$$⊢y\in \left\{x|\phi \right\}\to \forall xy\in \left\{x|\phi \right\}$$