Theorem breqtrrdi

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

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

Proof

Step	Hyp	Ref	Expression
1		breqtrrdi.1	|- ( ph -> A R B )
2		breqtrrdi.2	|- C = B
3	2	eqcomi	|- B = C
4	1 3	breqtrdi	|- ( ph -> A R C )