Theorem eqeq12dOLD

Description: Obsolete version of eqeq12d as of 23-Oct-2024. (Contributed by NM, 5-Aug-1993) (Proof shortened by Andrew Salmon, 25-May-2011) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	eqeq12dOLD.1	|- ( ph -> A = B )
	eqeq12dOLD.2	|- ( ph -> C = D )
Assertion	eqeq12dOLD	|- ( ph -> ( A = C <-> B = D ) )

Proof

Step	Hyp	Ref	Expression
1		eqeq12dOLD.1	|- ( ph -> A = B )
2		eqeq12dOLD.2	|- ( ph -> C = D )
3		eqeq12OLD	|- ( ( A = B /\ C = D ) -> ( A = C <-> B = D ) )
4	1 2 3	syl2anc	|- ( ph -> ( A = C <-> B = D ) )