Theorem eqbrtrdi

Description: A chained equality inference for a binary relation. (Contributed by NM, 12-Oct-1999)

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

Proof

Step	Hyp	Ref	Expression
1		eqbrtrdi.1	|- ( ph -> A = B )
2		eqbrtrdi.2	|- B R C
3	1	breq1d	|- ( ph -> ( A R C <-> B R C ) )
4	2 3	mpbiri	|- ( ph -> A R C )