Theorem eqeqan12dALT

Description: Alternate proof of eqeqan12d . This proof has one more step but one fewer essential step. (Contributed by NM, 9-Aug-1994) (Proof shortened by Andrew Salmon, 25-May-2011) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	eqeqan12dALT.1	|- ( ph -> A = B )
	eqeqan12dALT.2	|- ( ps -> C = D )
Assertion	eqeqan12dALT	|- ( ( ph /\ ps ) -> ( A = C <-> B = D ) )

Proof

Step	Hyp	Ref	Expression
1		eqeqan12dALT.1	|- ( ph -> A = B )
2		eqeqan12dALT.2	|- ( ps -> C = D )
3		eqeq12	|- ( ( A = B /\ C = D ) -> ( A = C <-> B = D ) )
4	1 2 3	syl2an	|- ( ( ph /\ ps ) -> ( A = C <-> B = D ) )