Theorem breqtrd

Description: Substitution of equal classes into a binary relation. (Contributed by NM, 24-Oct-1999)

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

Proof

Step	Hyp	Ref	Expression
1		breqtrd.1	|- ( ph -> A R B )
2		breqtrd.2	|- ( ph -> B = C )
3	2	breq2d	|- ( ph -> ( A R B <-> A R C ) )
4	1 3	mpbid	|- ( ph -> A R C )