Theorem xnegcli

Description: Closure of extended real negative. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypothesis	xnegcli.1	⊢ 𝐴 ∈ ℝ*
Assertion	xnegcli	⊢ -𝑒 𝐴 ∈ ℝ*

Proof

Step	Hyp	Ref	Expression
1		xnegcli.1	⊢ 𝐴 ∈ ℝ*
2		xnegcl	⊢ ( 𝐴 ∈ ℝ* → -𝑒 𝐴 ∈ ℝ* )
3	1 2	ax-mp	⊢ -𝑒 𝐴 ∈ ℝ*