Metamath Proof Explorer

Theorem 3anrot

Description: Rotation law for triple conjunction. (Contributed by NM, 8-Apr-1994) (Proof shortened by Wolf Lammen, 9-Jun-2022)

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

Proof

Step Hyp Ref Expression
1 3ancoma 
 |-  ( ( ph /\ ps /\ ch ) <-> ( ps /\ ph /\ ch ) )
2 3ancomb 
 |-  ( ( ps /\ ph /\ ch ) <-> ( ps /\ ch /\ ph ) )
3 1 2 bitri 
 |-  ( ( ph /\ ps /\ ch ) <-> ( ps /\ ch /\ ph ) )