Theorem eqbrtrrdi

Description: A chained equality inference for a binary relation. (Contributed by NM, 4-Jan-2006)

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

Proof

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