This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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*