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Metamath Proof Explorer

Theorem recclzi

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

		Ref	Expression
	Hypothesis	divclz.1	$⊢ A \in ℂ$
	Assertion	recclzi	$⊢ A \neq 0 \to \frac{1}{A} \in ℂ$

Step	Hyp	Ref	Expression
1		divclz.1	$⊢ A \in ℂ$
2		reccl	$⊢ (A \in ℂ \land A \neq 0) \to \frac{1}{A} \in ℂ$
3	1 2	mpan	$⊢ A \neq 0 \to \frac{1}{A} \in ℂ$