This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem recne0zi

Description: The reciprocal of a nonzero number is nonzero. (Contributed by NM, 14-May-1999)

		Ref	Expression
	Hypothesis	divclz.1	$⊢ A \in ℂ$
	Assertion	recne0zi	$⊢ A \neq 0 \to \frac{1}{A} \neq 0$

Step	Hyp	Ref	Expression
1		divclz.1	$⊢ A \in ℂ$
2		recne0	$⊢ (A \in ℂ \land A \neq 0) \to \frac{1}{A} \neq 0$
3	1 2	mpan	$⊢ A \neq 0 \to \frac{1}{A} \neq 0$