Metamath Proof Explorer

Theorem 3ancomb

Description: Commutation law for triple conjunction. (Contributed by NM, 21-Apr-1994) (Revised to shorten 3anrot by Wolf Lammen, 9-Jun-2022.)

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

Proof

Step Hyp Ref Expression
1 df-3an 
 |-  ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
2 3anan32 
 |-  ( ( ph /\ ch /\ ps ) <-> ( ( ph /\ ps ) /\ ch ) )
3 1 2 bitr4i 
 |-  ( ( ph /\ ps /\ ch ) <-> ( ph /\ ch /\ ps ) )