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