Theorem breqdi

Description: Equality deduction for a binary relation. (Contributed by Thierry Arnoux, 5-Oct-2020)

	Ref	Expression
Hypotheses	breq1d.1	|- ( ph -> A = B )
	breqdi.1	|- ( ph -> C A D )
Assertion	breqdi	|- ( ph -> C B D )

Proof

Step	Hyp	Ref	Expression
1		breq1d.1	|- ( ph -> A = B )
2		breqdi.1	|- ( ph -> C A D )
3	1	breqd	|- ( ph -> ( C A D <-> C B D ) )
4	2 3	mpbid	|- ( ph -> C B D )