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Metamath Proof Explorer

Theorem negcld

Description: Closure law for negative. (Contributed by Mario Carneiro, 27-May-2016)

		Ref	Expression
	Hypothesis	negidd.1	$⊢ φ \to A \in ℂ$
	Assertion	negcld	$⊢ φ \to - A \in ℂ$

Step	Hyp	Ref	Expression
1		negidd.1	$⊢ φ \to A \in ℂ$
2		negcl	$⊢ A \in ℂ \to - A \in ℂ$
3	1 2	syl	$⊢ φ \to - A \in ℂ$