Theorem dmqseq

Description: Equality theorem for domain quotient. (Contributed by Peter Mazsa, 17-Apr-2019)

	Ref	Expression
Assertion	dmqseq	⊢ ( 𝑅 = 𝑆 → ( dom 𝑅 / 𝑅 ) = ( dom 𝑆 / 𝑆 ) )

Proof

Step	Hyp	Ref	Expression
1		dmeq	⊢ ( 𝑅 = 𝑆 → dom 𝑅 = dom 𝑆 )
2		qseq12	⊢ ( ( dom 𝑅 = dom 𝑆 ∧ 𝑅 = 𝑆 ) → ( dom 𝑅 / 𝑅 ) = ( dom 𝑆 / 𝑆 ) )
3	1 2	mpancom	⊢ ( 𝑅 = 𝑆 → ( dom 𝑅 / 𝑅 ) = ( dom 𝑆 / 𝑆 ) )