Theorem breq123d

Description: Equality deduction for a binary relation. (Contributed by NM, 29-Oct-2011)

	Ref	Expression
Hypotheses	breq1d.1	|- ( ph -> A = B )
	breq123d.2	|- ( ph -> R = S )
	breq123d.3	|- ( ph -> C = D )
Assertion	breq123d	|- ( ph -> ( A R C <-> B S D ) )

Proof

Step	Hyp	Ref	Expression
1		breq1d.1	|- ( ph -> A = B )
2		breq123d.2	|- ( ph -> R = S )
3		breq123d.3	|- ( ph -> C = D )
4	1 3	breq12d	|- ( ph -> ( A R C <-> B R D ) )
5	2	breqd	|- ( ph -> ( B R D <-> B S D ) )
6	4 5	bitrd	|- ( ph -> ( A R C <-> B S D ) )