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Metamath Proof Explorer

Theorem gt0ne0i

Description: Positive means nonzero (useful for ordering theorems involving division). (Contributed by NM, 16-Sep-1999)

		Ref	Expression
	Hypothesis	lt2.1	$⊢ A \in ℝ$
	Assertion	gt0ne0i	$⊢ 0 < A \to A \neq 0$

Step	Hyp	Ref	Expression
1		lt2.1	$⊢ A \in ℝ$
2		0re	$⊢ 0 \in ℝ$
3	2 1	ltnei	$⊢ 0 < A \to A \neq 0$