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Metamath Proof Explorer

Theorem eldifn

Description: Implication of membership in a class difference. (Contributed by NM, 3-May-1994)

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

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