Metamath Proof Explorer


Theorem mulassnni

Description: Associative law for multiplication. (Contributed by metakunt, 25-Apr-2024)

Ref Expression
Hypotheses mulassnni.1 ⊢ A ∈ ℕ
mulassnni.2 ⊢ B ∈ ℕ
mulassnni.3 ⊢ C ∈ ℕ
Assertion mulassnni ⊢ A ⁢ B ⁢ C = A ⁢ B ⁢ C

Proof

Step Hyp Ref Expression
1 mulassnni.1 ⊢ A ∈ ℕ
2 mulassnni.2 ⊢ B ∈ ℕ
3 mulassnni.3 ⊢ C ∈ ℕ
4 1 nncni ⊢ A ∈ ℂ
5 2 nncni ⊢ B ∈ ℂ
6 3 nncni ⊢ C ∈ ℂ
7 4 5 6 mulassi ⊢ A ⁢ B ⁢ C = A ⁢ B ⁢ C