Metamath Proof Explorer

Theorem 3anan32

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

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

Proof

Step Hyp Ref Expression
1 df-3an ⊢ φ ∧ ψ ∧ χ ↔ φ ∧ ψ ∧ χ
2 an32 ⊢ φ ∧ ψ ∧ χ ↔ φ ∧ χ ∧ ψ
3 1 2 bitri ⊢ φ ∧ ψ ∧ χ ↔ φ ∧ χ ∧ ψ