Metamath Proof Explorer

Theorem an13

Description: A rearrangement of conjuncts. (Contributed by NM, 24-Jun-2012) (Proof shortened by Wolf Lammen, 31-Dec-2012)

Ref Expression
Assertion an13 ⊢φ∧ψ∧χ↔χ∧ψ∧φ

Proof

Step Hyp Ref Expression
1 an21 ⊢ψ∧φ∧χ↔φ∧ψ∧χ
2 ancom ⊢ψ∧φ∧χ↔χ∧ψ∧φ
3 1 2 bitr3i ⊢φ∧ψ∧χ↔χ∧ψ∧φ