Theorem eqbrtrrd

Description: Substitution of equal classes into a binary relation. (Contributed by NM, 24-Oct-1999)

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

Proof

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