Theorem negrebi

Description: The negative of a real is real. (Contributed by NM, 11-Aug-1999)

	Ref	Expression
Hypothesis	negidi.1	⊢ 𝐴 ∈ ℂ
Assertion	negrebi	⊢ ( - 𝐴 ∈ ℝ ↔ 𝐴 ∈ ℝ )

Proof

Step	Hyp	Ref	Expression
1		negidi.1	⊢ 𝐴 ∈ ℂ
2		negreb	⊢ ( 𝐴 ∈ ℂ → ( - 𝐴 ∈ ℝ ↔ 𝐴 ∈ ℝ ) )
3	1 2	ax-mp	⊢ ( - 𝐴 ∈ ℝ ↔ 𝐴 ∈ ℝ )