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	⊢ ( ( dom 𝑅 / 𝑅 ) = 𝐴 → ¬ ∅ ∈ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		n0eldmqs	⊢ ¬ ∅ ∈ ( dom 𝑅 / 𝑅 )
2		eleq2	⊢ ( ( dom 𝑅 / 𝑅 ) = 𝐴 → ( ∅ ∈ ( dom 𝑅 / 𝑅 ) ↔ ∅ ∈ 𝐴 ) )
3	1 2	mtbii	⊢ ( ( dom 𝑅 / 𝑅 ) = 𝐴 → ¬ ∅ ∈ 𝐴 )