Theorem breqan12d

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	breqan12d	|- ( ( ph /\ ps ) -> ( A R C <-> B R D ) )

Proof

Step	Hyp	Ref	Expression
1		breq1d.1	|- ( ph -> A = B )
2		breqan12i.2	|- ( ps -> C = D )
3		breq12	|- ( ( A = B /\ C = D ) -> ( A R C <-> B R D ) )
4	1 2 3	syl2an	|- ( ( ph /\ ps ) -> ( A R C <-> B R D ) )