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 ∈ ℂ
Assertion	negnegi	⊢ - - 𝐴 = 𝐴

Proof

Step	Hyp	Ref	Expression
1		negidi.1	⊢ 𝐴 ∈ ℂ
2		negneg	⊢ ( 𝐴 ∈ ℂ → - - 𝐴 = 𝐴 )
3	1 2	ax-mp	⊢ - - 𝐴 = 𝐴