Metamath Proof Explorer

Theorem an32

Description: A rearrangement of conjuncts. (Contributed by NM, 12-Mar-1995) (Proof shortened by Wolf Lammen, 25-Dec-2012)

Ref Expression
Assertion an32 ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜓 ) )

Proof

Step Hyp Ref Expression
1 an21 ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ↔ ( 𝜓 ∧ ( 𝜑 ∧ 𝜒 ) ) )
2 1 biancomi ⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜓 ) )