Theorem rspcvOLD

Description: Obsolete version of rspcv as of 12-Dec-2023. Restricted specialization, using implicit substitution. (Contributed by NM, 26-May-1998) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	rspcv.1	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
Assertion	rspcvOLD	$$⊢A\in B\to \left(\forall x\in B\phi \to \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		rspcv.1	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
2		nfv	$$⊢Ⅎx\psi$$
3	2 1	rspc	$$⊢A\in B\to \left(\forall x\in B\phi \to \psi \right)$$