Theorem breqan12rd

Description: Equality deduction for a binary relation. (Contributed by NM, 8-Feb-1996)

	Ref	Expression
Hypotheses	breq1d.1	|- ( ph -> A = B )
	breqan12i.2	|- ( ps -> C = D )
Assertion	breqan12rd	|- ( ( ps /\ ph ) -> ( A R C <-> B R D ) )

Proof

Step	Hyp	Ref	Expression
1		breq1d.1	|- ( ph -> A = B )
2		breqan12i.2	|- ( ps -> C = D )
3	1 2	breqan12d	|- ( ( ph /\ ps ) -> ( A R C <-> B R D ) )
4	3	ancoms	|- ( ( ps /\ ph ) -> ( A R C <-> B R D ) )