Metamath Proof Explorer


Theorem bnj256

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Assertion bnj256
|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ph /\ ps ) /\ ( ch /\ th ) ) )

Proof

Step Hyp Ref Expression
1 bnj248
 |-  ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ( ph /\ ps ) /\ ch ) /\ th ) )
2 anass
 |-  ( ( ( ( ph /\ ps ) /\ ch ) /\ th ) <-> ( ( ph /\ ps ) /\ ( ch /\ th ) ) )
3 1 2 bitri
 |-  ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ph /\ ps ) /\ ( ch /\ th ) ) )