Theorem dmqseqd

Description: Equality theorem for domain quotient set, deduction version. (Contributed by Peter Mazsa, 23-Apr-2021)

	Ref	Expression
Hypothesis	dmqseqd.1	⊢ ( 𝜑 → 𝑅 = 𝑆 )
Assertion	dmqseqd	⊢ ( 𝜑 → ( dom 𝑅 / 𝑅 ) = ( dom 𝑆 / 𝑆 ) )

Proof

Step	Hyp	Ref	Expression
1		dmqseqd.1	⊢ ( 𝜑 → 𝑅 = 𝑆 )
2		dmqseq	⊢ ( 𝑅 = 𝑆 → ( dom 𝑅 / 𝑅 ) = ( dom 𝑆 / 𝑆 ) )
3	1 2	syl	⊢ ( 𝜑 → ( dom 𝑅 / 𝑅 ) = ( dom 𝑆 / 𝑆 ) )