Metamath Proof Explorer

Theorem 3anan32

Description: Convert triple conjunction to conjunction, then commute. (Contributed by Jonathan Ben-Naim, 3-Jun-2011)

Ref Expression
Assertion 3anan32 
|- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ch ) /\ ps ) )

Proof

Step Hyp Ref Expression
1 df-3an 
 |-  ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ch ) )
2 an32 
 |-  ( ( ( ph /\ ps ) /\ ch ) <-> ( ( ph /\ ch ) /\ ps ) )
3 1 2 bitri 
 |-  ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ch ) /\ ps ) )