Metamath Proof Explorer

Theorem 3anan12

Description: Convert triple conjunction to conjunction, then commute. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Proof shortened by Andrew Salmon, 14-Jun-2011) (Revised to shorten 3ancoma by Wolf Lammen, 5-Jun-2022.)

Ref Expression
Assertion 3anan12 ⊢ φ ∧ ψ ∧ χ ↔ ψ ∧ φ ∧ χ

Proof

Step Hyp Ref Expression
1 3anass ⊢ φ ∧ ψ ∧ χ ↔ φ ∧ ψ ∧ χ
2 an12 ⊢ φ ∧ ψ ∧ χ ↔ ψ ∧ φ ∧ χ
3 1 2 bitri ⊢ φ ∧ ψ ∧ χ ↔ ψ ∧ φ ∧ χ