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Metamath Proof Explorer

Theorem ssrexvOLD

Description: Obsolete version of ssrexv as of 19-May-2025. (Contributed by NM, 11-Jan-2007) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	ssrexvOLD	$⊢ A \subseteq B \to (\exists x \in A φ \to \exists x \in B φ)$

Proof

Step	Hyp	Ref	Expression
1		ssel	$⊢ A \subseteq B \to (x \in A \to x \in B)$
2	1	anim1d	$⊢ A \subseteq B \to ((x \in A \land φ) \to (x \in B \land φ))$
3	2	reximdv2	$⊢ A \subseteq B \to (\exists x \in A φ \to \exists x \in B φ)$