Theorem xmulcl

Description: Closure of extended real multiplication. (Contributed by Mario Carneiro, 20-Aug-2015)

	Ref	Expression
Assertion	xmulcl	⊢ ( ( 𝐴 ∈ ℝ* ∧ 𝐵 ∈ ℝ* ) → ( 𝐴 ·e 𝐵 ) ∈ ℝ* )

Proof

Step	Hyp	Ref	Expression
1		xmulf	⊢ ·e : ( ℝ* × ℝ* ) ⟶ ℝ*
2	1	fovcl	⊢ ( ( 𝐴 ∈ ℝ* ∧ 𝐵 ∈ ℝ* ) → ( 𝐴 ·e 𝐵 ) ∈ ℝ* )