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Metamath Proof Explorer

Theorem ovprc1

Description: The value of an operation when the first argument is a proper class. (Contributed by NM, 16-Jun-2004)

		Ref	Expression
	Hypothesis	ovprc1.1	$⊢ Rel dom F$
	Assertion	ovprc1	$⊢ \neg A \in V \to A F B = \emptyset$

Step	Hyp	Ref	Expression
1		ovprc1.1	$⊢ Rel dom F$
2		simpl	$⊢ (A \in V \land B \in V) \to A \in V$
3	1	ovprc	$⊢ \neg (A \in V \land B \in V) \to A F B = \emptyset$
4	2 3	nsyl5	$⊢ \neg A \in V \to A F B = \emptyset$