# Metamath Proof Explorer

## Theorem bnj290

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

Ref Expression
Assertion bnj290 ${⊢}\left({\phi }\wedge {\psi }\wedge {\chi }\wedge {\theta }\right)↔\left({\phi }\wedge {\chi }\wedge {\theta }\wedge {\psi }\right)$

### Proof

Step Hyp Ref Expression
1 3anrot ${⊢}\left({\psi }\wedge {\chi }\wedge {\theta }\right)↔\left({\chi }\wedge {\theta }\wedge {\psi }\right)$
2 1 anbi2i ${⊢}\left({\phi }\wedge \left({\psi }\wedge {\chi }\wedge {\theta }\right)\right)↔\left({\phi }\wedge \left({\chi }\wedge {\theta }\wedge {\psi }\right)\right)$
3 bnj252 ${⊢}\left({\phi }\wedge {\psi }\wedge {\chi }\wedge {\theta }\right)↔\left({\phi }\wedge \left({\psi }\wedge {\chi }\wedge {\theta }\right)\right)$
4 bnj252 ${⊢}\left({\phi }\wedge {\chi }\wedge {\theta }\wedge {\psi }\right)↔\left({\phi }\wedge \left({\chi }\wedge {\theta }\wedge {\psi }\right)\right)$
5 2 3 4 3bitr4i ${⊢}\left({\phi }\wedge {\psi }\wedge {\chi }\wedge {\theta }\right)↔\left({\phi }\wedge {\chi }\wedge {\theta }\wedge {\psi }\right)$