Theorem mulcli

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

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

Proof

Step	Hyp	Ref	Expression
1		axi.1	⊢ 𝐴 ∈ ℂ
2		axi.2	⊢ 𝐵 ∈ ℂ
3		mulcl	⊢ ( ( 𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ ) → ( 𝐴 · 𝐵 ) ∈ ℂ )
4	1 2 3	mp2an	⊢ ( 𝐴 · 𝐵 ) ∈ ℂ