Theorem n0eldmqseq

Description: The empty set is not an element of a domain quotient. (Contributed by Peter Mazsa, 3-Nov-2018)

	Ref	Expression
Assertion	n0eldmqseq	$$⊢\mathrm{dom}R/R=A\to \neg \varnothing \in A$$

Proof

Step	Hyp	Ref	Expression
1		n0eldmqs	$$⊢\neg \varnothing \in \left(\mathrm{dom}R/R\right)$$
2		eleq2	$$⊢\mathrm{dom}R/R=A\to \left(\varnothing \in \left(\mathrm{dom}R/R\right)\leftrightarrow \varnothing \in A\right)$$
3	1 2	mtbii	$$⊢\mathrm{dom}R/R=A\to \neg \varnothing \in A$$