Theorem breqtrrid

Description: A chained equality inference for a binary relation. (Contributed by NM, 24-Apr-2005)

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

Proof

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