Metamath Proof Explorer

Theorem 3ancoma

Description: Commutation law for triple conjunction. (Contributed by NM, 21-Apr-1994) (Proof shortened by Wolf Lammen, 5-Jun-2022)

Ref Expression
Assertion 3ancoma 
|- ( ( ph /\ ps /\ ch ) <-> ( ps /\ ph /\ ch ) )

Proof

Step Hyp Ref Expression
1 3anan12 
 |-  ( ( ph /\ ps /\ ch ) <-> ( ps /\ ( ph /\ ch ) ) )
2 3anass 
 |-  ( ( ps /\ ph /\ ch ) <-> ( ps /\ ( ph /\ ch ) ) )
3 1 2 bitr4i 
 |-  ( ( ph /\ ps /\ ch ) <-> ( ps /\ ph /\ ch ) )