Theorem dmqseqd

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

	Ref	Expression
Hypothesis	dmqseqd.1	|- ( ph -> R = S )
Assertion	dmqseqd	|- ( ph -> ( dom R /. R ) = ( dom S /. S ) )

Proof

Step	Hyp	Ref	Expression
1		dmqseqd.1	|- ( ph -> R = S )
2		dmqseq	|- ( R = S -> ( dom R /. R ) = ( dom S /. S ) )
3	1 2	syl	|- ( ph -> ( dom R /. R ) = ( dom S /. S ) )