Theorem negrebi

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

	Ref	Expression
Hypothesis	negidi.1	$$⊢A\in ℂ$$
Assertion	negrebi	$$⊢-A\in ℝ\leftrightarrow A\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		negidi.1	$$⊢A\in ℂ$$
2		negreb	$$⊢A\in ℂ\to \left(-A\in ℝ\leftrightarrow A\in ℝ\right)$$
3	1 2	ax-mp	$$⊢-A\in ℝ\leftrightarrow A\in ℝ$$