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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