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Metamath Proof Explorer

Theorem reccl

Description: Closure law for reciprocal. (Contributed by NM, 30-Apr-2005)

		Ref	Expression
	Assertion	reccl	$⊢ (A \in ℂ \land A \neq 0) \to \frac{1}{A} \in ℂ$

Step	Hyp	Ref	Expression
1		ax-1cn	$⊢ 1 \in ℂ$
2		divcl	$⊢ (1 \in ℂ \land A \in ℂ \land A \neq 0) \to \frac{1}{A} \in ℂ$
3	1 2	mp3an1	$⊢ (A \in ℂ \land A \neq 0) \to \frac{1}{A} \in ℂ$