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Metamath Proof Explorer

Theorem n0eldmqs

Description: The empty set is not an element of a domain quotient. (Contributed by Peter Mazsa, 2-Mar-2018)

		Ref	Expression
	Assertion	n0eldmqs	$⊢ \neg \emptyset \in (dom R / R)$

Step	Hyp	Ref	Expression
1		ssid	$⊢ dom R \subseteq dom R$
2		n0elqs	$⊢ \neg \emptyset \in (dom R / R) \leftrightarrow dom R \subseteq dom R$
3	1 2	mpbir	$⊢ \neg \emptyset \in (dom R / R)$