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Metamath Proof Explorer

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	$⊢ - (- A) = A$

Proof

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