Metamath Proof Explorer

Theorem 3ancoma

Description: Commutation law for triple conjunction. (Contributed by NM, 21-Apr-1994) (Proof shortened by Wolf Lammen, 5-Jun-2022)

Ref Expression
Assertion 3ancoma ⊢φ∧ψ∧χ↔ψ∧φ∧χ

Proof

Step Hyp Ref Expression
1 3anan12 ⊢φ∧ψ∧χ↔ψ∧φ∧χ
2 3anass ⊢ψ∧φ∧χ↔ψ∧φ∧χ
3 1 2 bitr4i ⊢φ∧ψ∧χ↔ψ∧φ∧χ