Theorem qseq12d

Description: Equality theorem for quotient set, deduction form. (Contributed by Steven Nguyen, 30-Apr-2023)

	Ref	Expression
Hypotheses	qseq12d.1	|- ( ph -> A = B )
	qseq12d.2	|- ( ph -> C = D )
Assertion	qseq12d	|- ( ph -> ( A /. C ) = ( B /. D ) )

Proof

Step	Hyp	Ref	Expression
1		qseq12d.1	|- ( ph -> A = B )
2		qseq12d.2	|- ( ph -> C = D )
3		qseq12	|- ( ( A = B /\ C = D ) -> ( A /. C ) = ( B /. D ) )
4	1 2 3	syl2anc	|- ( ph -> ( A /. C ) = ( B /. D ) )