Theorem dmqseqeq1

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

	Ref	Expression
Assertion	dmqseqeq1	⊢ ( 𝑅 = 𝑆 → ( ( dom 𝑅 / 𝑅 ) = 𝐴 ↔ ( dom 𝑆 / 𝑆 ) = 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		dmqseq	⊢ ( 𝑅 = 𝑆 → ( dom 𝑅 / 𝑅 ) = ( dom 𝑆 / 𝑆 ) )
2	1	eqeq1d	⊢ ( 𝑅 = 𝑆 → ( ( dom 𝑅 / 𝑅 ) = 𝐴 ↔ ( dom 𝑆 / 𝑆 ) = 𝐴 ) )