Theorem 3brtr3d

Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 18-Oct-1999)

	Ref	Expression
Hypotheses	3brtr3d.1	|- ( ph -> A R B )
	3brtr3d.2	|- ( ph -> A = C )
	3brtr3d.3	|- ( ph -> B = D )
Assertion	3brtr3d	|- ( ph -> C R D )

Proof

Step	Hyp	Ref	Expression
1		3brtr3d.1	|- ( ph -> A R B )
2		3brtr3d.2	|- ( ph -> A = C )
3		3brtr3d.3	|- ( ph -> B = D )
4	2 3	breq12d	|- ( ph -> ( A R B <-> C R D ) )
5	1 4	mpbid	|- ( ph -> C R D )