Metamath Proof Explorer

Theorem anass

Description: Associative law for conjunction. Theorem *4.32 of WhiteheadRussell p. 118. (Contributed by NM, 21-Jun-1993) (Proof shortened by Wolf Lammen, 24-Nov-2012)

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

Proof

Step Hyp Ref Expression
1 id ⊢ φ ∧ ψ ∧ χ → φ ∧ ψ ∧ χ
2 1 anassrs ⊢ φ ∧ ψ ∧ χ → φ ∧ ψ ∧ χ
3 id ⊢ φ ∧ ψ ∧ χ → φ ∧ ψ ∧ χ
4 3 anasss ⊢ φ ∧ ψ ∧ χ → φ ∧ ψ ∧ χ
5 2 4 impbii ⊢ φ ∧ ψ ∧ χ ↔ φ ∧ ψ ∧ χ