Theorem dmqseqeq1i

Description: Equality theorem for domain quotient, inference version. (Contributed by Peter Mazsa, 26-Sep-2021)

	Ref	Expression
Hypothesis	dmqseqeq1i.1	|- R = S
Assertion	dmqseqeq1i	|- ( ( dom R /. R ) = A <-> ( dom S /. S ) = A )

Proof

Step	Hyp	Ref	Expression
1		dmqseqeq1i.1	|- R = S
2		dmqseqeq1	|- ( R = S -> ( ( dom R /. R ) = A <-> ( dom S /. S ) = A ) )
3	1 2	ax-mp	|- ( ( dom R /. R ) = A <-> ( dom S /. S ) = A )