Metamath Proof Explorer


Theorem ancom

Description: Commutative law for conjunction. Theorem *4.3 of WhiteheadRussell p. 118. (Contributed by NM, 25-Jun-1998) (Proof shortened by Wolf Lammen, 4-Nov-2012)

Ref Expression
Assertion ancom
|- ( ( ph /\ ps ) <-> ( ps /\ ph ) )

Proof

Step Hyp Ref Expression
1 pm3.22
 |-  ( ( ph /\ ps ) -> ( ps /\ ph ) )
2 pm3.22
 |-  ( ( ps /\ ph ) -> ( ph /\ ps ) )
3 1 2 impbii
 |-  ( ( ph /\ ps ) <-> ( ps /\ ph ) )