Theorem mulcomli

Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994)

	Ref	Expression
Hypotheses	axi.1	⊢ 𝐴 ∈ ℂ
	axi.2	⊢ 𝐵 ∈ ℂ
	mulcomli.3	⊢ ( 𝐴 · 𝐵 ) = 𝐶
Assertion	mulcomli	⊢ ( 𝐵 · 𝐴 ) = 𝐶

Proof

Step	Hyp	Ref	Expression
1		axi.1	⊢ 𝐴 ∈ ℂ
2		axi.2	⊢ 𝐵 ∈ ℂ
3		mulcomli.3	⊢ ( 𝐴 · 𝐵 ) = 𝐶
4	2 1	mulcomi	⊢ ( 𝐵 · 𝐴 ) = ( 𝐴 · 𝐵 )
5	4 3	eqtri	⊢ ( 𝐵 · 𝐴 ) = 𝐶