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Metamath Proof Explorer

Theorem 3anrot

Description: Rotation law for triple conjunction. (Contributed by NM, 8-Apr-1994) (Proof shortened by Wolf Lammen, 9-Jun-2022)

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

Proof

Step Hyp Ref Expression
1 3ancoma ⊢ φ ∧ ψ ∧ χ ↔ ψ ∧ φ ∧ χ
2 3ancomb ⊢ ψ ∧ φ ∧ χ ↔ ψ ∧ χ ∧ φ
3 1 2 bitri ⊢ φ ∧ ψ ∧ χ ↔ ψ ∧ χ ∧ φ