Theorem dmqsex

Description: Sethood of the domain quotient under sethood of R . (Contributed by Peter Mazsa, 2-Nov-2018)

	Ref	Expression
Assertion	dmqsex	⊢ ( 𝑅 ∈ 𝑉 → ( dom 𝑅 / 𝑅 ) ∈ V )

Proof

Step	Hyp	Ref	Expression
1		dmexg	⊢ ( 𝑅 ∈ 𝑉 → dom 𝑅 ∈ V )
2		qsexg	⊢ ( dom 𝑅 ∈ V → ( dom 𝑅 / 𝑅 ) ∈ V )
3	1 2	syl	⊢ ( 𝑅 ∈ 𝑉 → ( dom 𝑅 / 𝑅 ) ∈ V )