Metamath Proof Explorer

Theorem bnj170

Description: /\ -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Andrew Salmon, 14-Jun-2011) (New usage is discouraged.)

Ref Expression
Assertion bnj170 ⊢ φ ∧ ψ ∧ χ ↔ ψ ∧ χ ∧ φ

Proof

Step Hyp Ref Expression
1 3anrot ⊢ φ ∧ ψ ∧ χ ↔ ψ ∧ χ ∧ φ
2 df-3an ⊢ ψ ∧ χ ∧ φ ↔ ψ ∧ χ ∧ φ
3 1 2 bitri ⊢ φ ∧ ψ ∧ χ ↔ ψ ∧ χ ∧ φ