Theorem mulcomnni

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

	Ref	Expression
Hypotheses	mulcomnni.1	⊢ 𝐴 ∈ ℕ
	mulcomnni.2	⊢ 𝐵 ∈ ℕ
Assertion	mulcomnni	⊢ ( 𝐴 · 𝐵 ) = ( 𝐵 · 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		mulcomnni.1	⊢ 𝐴 ∈ ℕ
2		mulcomnni.2	⊢ 𝐵 ∈ ℕ
3	1	nncni	⊢ 𝐴 ∈ ℂ
4	2	nncni	⊢ 𝐵 ∈ ℂ
5	3 4	mulcomi	⊢ ( 𝐴 · 𝐵 ) = ( 𝐵 · 𝐴 )