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Metamath Proof Explorer

Theorem rspe

Description: Restricted specialization. (Contributed by NM, 12-Oct-1999)

		Ref	Expression
	Assertion	rspe	$⊢ (x \in A \land φ) \to \exists x \in A φ$

Step	Hyp	Ref	Expression
1		19.8a	$⊢ (x \in A \land φ) \to \exists x (x \in A \land φ)$
2		df-rex	$⊢ \exists x \in A φ \leftrightarrow \exists x (x \in A \land φ)$
3	1 2	sylibr	$⊢ (x \in A \land φ) \to \exists x \in A φ$