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Metamath Proof Explorer

Theorem eldifsni

Description: Membership in a set with an element removed. (Contributed by NM, 10-Mar-2015)

		Ref	Expression
	Assertion	eldifsni	$⊢ A \in (B ∖ \{C\}) \to A \neq C$

Step	Hyp	Ref	Expression
1		eldifsn	$⊢ A \in (B ∖ \{C\}) \leftrightarrow (A \in B \land A \neq C)$
2	1	simprbi	$⊢ A \in (B ∖ \{C\}) \to A \neq C$