Theorem breqtrrd

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

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

Proof

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