Metamath Proof Explorer

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 ) )