Theorem breq1dd

Description: Equality deduction for a binary relation. (Contributed by Thierry Arnoux, 10-Jan-2026)

	Ref	Expression
Hypotheses	breq1dd.1	|- ( ph -> A = B )
	breq1dd.2	|- ( ph -> A R C )
Assertion	breq1dd	|- ( ph -> B R C )

Proof

Step	Hyp	Ref	Expression
1		breq1dd.1	|- ( ph -> A = B )
2		breq1dd.2	|- ( ph -> A R C )
3	1	breq1d	|- ( ph -> ( A R C <-> B R C ) )
4	2 3	mpbid	|- ( ph -> B R C )