Metamath Proof Explorer


Theorem bnj446

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

Ref Expression
Assertion bnj446
|- ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ps /\ ch /\ th ) /\ ph ) )

Proof

Step Hyp Ref Expression
1 bnj345
 |-  ( ( ps /\ ch /\ th /\ ph ) <-> ( ph /\ ps /\ ch /\ th ) )
2 df-bnj17
 |-  ( ( ps /\ ch /\ th /\ ph ) <-> ( ( ps /\ ch /\ th ) /\ ph ) )
3 1 2 bitr3i
 |-  ( ( ph /\ ps /\ ch /\ th ) <-> ( ( ps /\ ch /\ th ) /\ ph ) )