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Metamath Proof Explorer

Theorem undefnel

Description: The undefined value generated from a set is not a member of the set. (Contributed by NM, 15-Sep-2011)

		Ref	Expression
	Assertion	undefnel	$⊢ S \in V \to Undef (S) \notin S$

Step	Hyp	Ref	Expression
1		undefnel2	$⊢ S \in V \to \neg Undef (S) \in S$
2		df-nel	$⊢ Undef (S) \notin S \leftrightarrow \neg Undef (S) \in S$
3	1 2	sylibr	$⊢ S \in V \to Undef (S) \notin S$