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Metamath Proof Explorer

Theorem eldifi

Description: Implication of membership in a class difference. (Contributed by NM, 29-Apr-1994)

		Ref	Expression
	Assertion	eldifi	$⊢ A \in (B ∖ C) \to A \in B$

Step	Hyp	Ref	Expression
1		eldif	$⊢ A \in (B ∖ C) \leftrightarrow (A \in B \land \neg A \in C)$
2	1	simplbi	$⊢ A \in (B ∖ C) \to A \in B$