Metamath Proof Explorer


Theorem xnegcld

Description: Closure of extended real negative. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypothesis xnegcld.1 ⊢ φ → A ∈ ℝ *
Assertion xnegcld ⊢ φ → − A ∈ ℝ *

Proof

Step Hyp Ref Expression
1 xnegcld.1 ⊢ φ → A ∈ ℝ *
2 xnegcl ⊢ A ∈ ℝ * → − A ∈ ℝ *
3 1 2 syl ⊢ φ → − A ∈ ℝ *