# Metamath Proof Explorer

## Theorem bnj268

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

Ref Expression
Assertion bnj268 ${⊢}\left({\phi }\wedge {\psi }\wedge {\chi }\wedge {\theta }\right)↔\left({\phi }\wedge {\chi }\wedge {\psi }\wedge {\theta }\right)$

### Proof

Step Hyp Ref Expression
1 3ancomb ${⊢}\left({\phi }\wedge {\psi }\wedge {\chi }\right)↔\left({\phi }\wedge {\chi }\wedge {\psi }\right)$
2 1 anbi1i ${⊢}\left(\left({\phi }\wedge {\psi }\wedge {\chi }\right)\wedge {\theta }\right)↔\left(\left({\phi }\wedge {\chi }\wedge {\psi }\right)\wedge {\theta }\right)$
3 df-bnj17 ${⊢}\left({\phi }\wedge {\psi }\wedge {\chi }\wedge {\theta }\right)↔\left(\left({\phi }\wedge {\psi }\wedge {\chi }\right)\wedge {\theta }\right)$
4 df-bnj17 ${⊢}\left({\phi }\wedge {\chi }\wedge {\psi }\wedge {\theta }\right)↔\left(\left({\phi }\wedge {\chi }\wedge {\psi }\right)\wedge {\theta }\right)$
5 2 3 4 3bitr4i ${⊢}\left({\phi }\wedge {\psi }\wedge {\chi }\wedge {\theta }\right)↔\left({\phi }\wedge {\chi }\wedge {\psi }\wedge {\theta }\right)$