Theorem 3brtr3g

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

	Ref	Expression
Hypotheses	3brtr3g.1	|- ( ph -> A R B )
	3brtr3g.2	|- A = C
	3brtr3g.3	|- B = D
Assertion	3brtr3g	|- ( ph -> C R D )

Proof

Step	Hyp	Ref	Expression
1		3brtr3g.1	|- ( ph -> A R B )
2		3brtr3g.2	|- A = C
3		3brtr3g.3	|- B = D
4	2 3	breq12i	|- ( A R B <-> C R D )
5	1 4	sylib	|- ( ph -> C R D )