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Metamath Proof Explorer

Theorem an31

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

Ref Expression
Assertion an31 ⊢ φ ∧ ψ ∧ χ ↔ χ ∧ ψ ∧ φ

Proof

Step Hyp Ref Expression
1 an13 ⊢ φ ∧ ψ ∧ χ ↔ χ ∧ ψ ∧ φ
2 anass ⊢ φ ∧ ψ ∧ χ ↔ φ ∧ ψ ∧ χ
3 anass ⊢ χ ∧ ψ ∧ φ ↔ χ ∧ ψ ∧ φ
4 1 2 3 3bitr4i ⊢ φ ∧ ψ ∧ χ ↔ χ ∧ ψ ∧ φ