Theorem mulcomnni

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

	Ref	Expression
Hypotheses	mulcomnni.1	$$⊢A\in \mathbb{N}$$
	mulcomnni.2	$$⊢B\in \mathbb{N}$$
Assertion	mulcomnni	$$⊢AB=BA$$

Proof

Step	Hyp	Ref	Expression
1		mulcomnni.1	$$⊢A\in \mathbb{N}$$
2		mulcomnni.2	$$⊢B\in \mathbb{N}$$
3	1	nncni	$$⊢A\in ℂ$$
4	2	nncni	$$⊢B\in ℂ$$
5	3 4	mulcomi	$$⊢AB=BA$$