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Metamath Proof Explorer

Theorem elin2d

Description: Elementhood in the first set of an intersection - deduction version. (Contributed by Thierry Arnoux, 3-May-2020)

		Ref	Expression
	Hypothesis	elin1d.1	$⊢ φ \to X \in (A \cap B)$
	Assertion	elin2d	$⊢ φ \to X \in B$

Step	Hyp	Ref	Expression
1		elin1d.1	$⊢ φ \to X \in (A \cap B)$
2		elinel2	$⊢ X \in (A \cap B) \to X \in B$
3	1 2	syl	$⊢ φ \to X \in B$