Theorem negnegd

Description: A number is equal to the negative of its negative. Theorem I.4 of Apostol p. 18. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypothesis	negidd.1	$$⊢\phi \to A\in ℂ$$
Assertion	negnegd	$$⊢\phi \to -\left(-A\right)=A$$

Proof

Step	Hyp	Ref	Expression
1		negidd.1	$$⊢\phi \to A\in ℂ$$
2		negneg	$$⊢A\in ℂ\to -\left(-A\right)=A$$
3	1 2	syl	$$⊢\phi \to -\left(-A\right)=A$$