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	$$⊢\neg \varnothing \in \left(\mathrm{dom}R/R\right)$$

Proof

Step	Hyp	Ref	Expression
1		ssid	$$⊢\mathrm{dom}R\subseteq \mathrm{dom}R$$
2		n0elqs	$$⊢\neg \varnothing \in \left(\mathrm{dom}R/R\right)\leftrightarrow \mathrm{dom}R\subseteq \mathrm{dom}R$$
3	1 2	mpbir	$$⊢\neg \varnothing \in \left(\mathrm{dom}R/R\right)$$