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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 → -𝑒 𝐴 ∈ ℝ* )

Proof

Step Hyp Ref Expression
1 xnegcld.1 ⊢ ( 𝜑 → 𝐴 ∈ ℝ* )
2 xnegcl ⊢ ( 𝐴 ∈ ℝ* → -𝑒 𝐴 ∈ ℝ* )
3 1 2 syl ⊢ ( 𝜑 → -𝑒 𝐴 ∈ ℝ* )