Theorem xmulcl

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

	Ref	Expression
Assertion	xmulcl	$$⊢\left(A\in {ℝ}^{*}\wedge B\in {ℝ}^{*}\right)\to A{\cdot }_{𝑒}B\in {ℝ}^{*}$$

Proof

Step	Hyp	Ref	Expression
1		xmulf	$$⊢{\cdot }_{𝑒}:{ℝ}^{*}\times {ℝ}^{*}⟶{ℝ}^{*}$$
2	1	fovcl	$$⊢\left(A\in {ℝ}^{*}\wedge B\in {ℝ}^{*}\right)\to A{\cdot }_{𝑒}B\in {ℝ}^{*}$$