Theorem 3brtr4g

Description: Substitution of equality into both sides of a binary relation. (Contributed by NM, 16-Jan-1997)

	Ref	Expression
Hypotheses	3brtr4g.1	|- ( ph -> A R B )
	3brtr4g.2	|- C = A
	3brtr4g.3	|- D = B
Assertion	3brtr4g	|- ( ph -> C R D )

Proof

Step	Hyp	Ref	Expression
1		3brtr4g.1	|- ( ph -> A R B )
2		3brtr4g.2	|- C = A
3		3brtr4g.3	|- D = B
4	2 3	breq12i	|- ( C R D <-> A R B )
5	1 4	sylibr	|- ( ph -> C R D )