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* )