Theorem hbab1OLD

Description: Obsolete version of hbab1 as of 25-Oct-2024. (Contributed by NM, 26-May-1993) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	hbab1OLD	$$⊢y\in \left\{x|\phi \right\}\to \forall xy\in \left\{x|\phi \right\}$$

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	$$⊢y\in \left\{x|\phi \right\}\to \forall xy\in \left\{x|\phi \right\}$$