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Metamath Proof Explorer

Theorem rspccv

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

		Ref	Expression
	Hypothesis	rspcv.1	$⊢ x = A \to (φ \leftrightarrow ψ)$
	Assertion	rspccv	$⊢ \forall x \in B φ \to (A \in B \to ψ)$

Step	Hyp	Ref	Expression
1		rspcv.1	$⊢ x = A \to (φ \leftrightarrow ψ)$
2	1	rspcv	$⊢ A \in B \to (\forall x \in B φ \to ψ)$
3	2	com12	$⊢ \forall x \in B φ \to (A \in B \to ψ)$