# Metamath Proof Explorer

## Theorem bnj251

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

Ref Expression
Assertion bnj251 ${⊢}\left({\phi }\wedge {\psi }\wedge {\chi }\wedge {\theta }\right)↔\left({\phi }\wedge \left({\psi }\wedge \left({\chi }\wedge {\theta }\right)\right)\right)$

### Proof

Step Hyp Ref Expression
1 bnj250 ${⊢}\left({\phi }\wedge {\psi }\wedge {\chi }\wedge {\theta }\right)↔\left({\phi }\wedge \left(\left({\psi }\wedge {\chi }\right)\wedge {\theta }\right)\right)$
2 anass ${⊢}\left(\left({\psi }\wedge {\chi }\right)\wedge {\theta }\right)↔\left({\psi }\wedge \left({\chi }\wedge {\theta }\right)\right)$
3 2 anbi2i ${⊢}\left({\phi }\wedge \left(\left({\psi }\wedge {\chi }\right)\wedge {\theta }\right)\right)↔\left({\phi }\wedge \left({\psi }\wedge \left({\chi }\wedge {\theta }\right)\right)\right)$
4 1 3 bitri ${⊢}\left({\phi }\wedge {\psi }\wedge {\chi }\wedge {\theta }\right)↔\left({\phi }\wedge \left({\psi }\wedge \left({\chi }\wedge {\theta }\right)\right)\right)$