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Metamath Proof Explorer

Theorem rsp

Description: Restricted specialization. (Contributed by NM, 17-Oct-1996)

		Ref	Expression
	Assertion	rsp	$⊢ \forall x \in A φ \to (x \in A \to φ)$

Step	Hyp	Ref	Expression
1		df-ral	$⊢ \forall x \in A φ \leftrightarrow \forall x (x \in A \to φ)$
2		sp	$⊢ \forall x (x \in A \to φ) \to (x \in A \to φ)$
3	1 2	sylbi	$⊢ \forall x \in A φ \to (x \in A \to φ)$