Theorem eqbrtrd

Description: Substitution of equal classes into a binary relation. (Contributed by NM, 8-Oct-1999)

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

Proof

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