Theorem negnegi

Description: A number is equal to the negative of its negative. Theorem I.4 of Apostol p. 18. (Contributed by NM, 8-Feb-1995) (Proof shortened by Andrew Salmon, 22-Oct-2011)

	Ref	Expression
Hypothesis	negidi.1	$$⊢A\in ℂ$$
Assertion	negnegi	$$⊢-\left(-A\right)=A$$

Proof

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