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Metamath Proof Explorer

Theorem 3ancomb

Description: Commutation law for triple conjunction. (Contributed by NM, 21-Apr-1994) (Revised to shorten 3anrot by Wolf Lammen, 9-Jun-2022.)

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

Proof

Step Hyp Ref Expression
1 df-3an ⊢ φ ∧ ψ ∧ χ ↔ φ ∧ ψ ∧ χ
2 3anan32 ⊢ φ ∧ χ ∧ ψ ↔ φ ∧ ψ ∧ χ
3 1 2 bitr4i ⊢ φ ∧ ψ ∧ χ ↔ φ ∧ χ ∧ ψ