Metamath Proof Explorer


Theorem eqeqan12dOLD

Description: Obsolete version of eqeqan12d as of 23-Oct-2024. (Contributed by NM, 9-Aug-1994) (Proof shortened by Andrew Salmon, 25-May-2011) (Proof shortened by Wolf Lammen, 20-Nov-2019) (New usage is discouraged.) (Proof modification is discouraged.)

Ref Expression
Hypotheses eqeqan12dOLD.1
|- ( ph -> A = B )
eqeqan12dOLD.2
|- ( ps -> C = D )
Assertion eqeqan12dOLD
|- ( ( ph /\ ps ) -> ( A = C <-> B = D ) )

Proof

Step Hyp Ref Expression
1 eqeqan12dOLD.1
 |-  ( ph -> A = B )
2 eqeqan12dOLD.2
 |-  ( ps -> C = D )
3 1 adantr
 |-  ( ( ph /\ ps ) -> A = B )
4 2 adantl
 |-  ( ( ph /\ ps ) -> C = D )
5 3 4 eqeq12dOLD
 |-  ( ( ph /\ ps ) -> ( A = C <-> B = D ) )