Metamath Proof Explorer

Theorem bnj252

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

Ref Expression
Assertion bnj252 
|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ( ps /\ ch /\ th ) ) )

Proof

Step Hyp Ref Expression
1 bnj250 
 |-  ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ( ( ps /\ ch ) /\ th ) ) )
2 df-3an 
 |-  ( ( ps /\ ch /\ th ) <-> ( ( ps /\ ch ) /\ th ) )
3 2 anbi2i 
 |-  ( ( ph /\ ( ps /\ ch /\ th ) ) <-> ( ph /\ ( ( ps /\ ch ) /\ th ) ) )
4 1 3 bitr4i 
 |-  ( ( ph /\ ps /\ ch /\ th ) <-> ( ph /\ ( ps /\ ch /\ th ) ) )