Metamath Proof Explorer

Theorem 3anan32

Description: Convert triple conjunction to conjunction, then commute. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Shortened by Garrett Katz, 15-Jun-2026.)

Ref Expression
Assertion 3anan32 ⊢ φ ∧ ψ ∧ χ ↔ φ ∧ χ ∧ ψ

Proof

Step Hyp Ref Expression
1 3anan12 ⊢ φ ∧ ψ ∧ χ ↔ ψ ∧ φ ∧ χ
2 1 biancomi ⊢ φ ∧ ψ ∧ χ ↔ φ ∧ χ ∧ ψ