Metamath Proof Explorer


Theorem anandi3

Description: Distribution of triple conjunction over conjunction. (Contributed by David A. Wheeler, 4-Nov-2018)

Ref Expression
Assertion anandi3
|- ( ( ph /\ ps /\ ch ) <-> ( ( ph /\ ps ) /\ ( ph /\ ch ) ) )

Proof

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