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Metamath Proof Explorer

Theorem negcl

Description: Closure law for negative. (Contributed by NM, 6-Aug-2003)

		Ref	Expression
	Assertion	negcl	$⊢ A \in ℂ \to - A \in ℂ$

Step	Hyp	Ref	Expression
1		df-neg	$⊢ - A = 0 - A$
2		0cn	$⊢ 0 \in ℂ$
3		subcl	$⊢ (0 \in ℂ \land A \in ℂ) \to 0 - A \in ℂ$
4	2 3	mpan	$⊢ A \in ℂ \to 0 - A \in ℂ$
5	1 4	eqeltrid	$⊢ A \in ℂ \to - A \in ℂ$