Theorem rspccv

Description: Restricted specialization, using implicit substitution. (Contributed by NM, 2-Feb-2006)

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

Proof

Step	Hyp	Ref	Expression
1		rspcv.1	$$⊢x=A\to \left(\phi \leftrightarrow \psi \right)$$
2	1	rspcv	$$⊢A\in B\to \left(\forall x\in B\phi \to \psi \right)$$
3	2	com12	$$⊢\forall x\in B\phi \to \left(A\in B\to \psi \right)$$