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Metamath Proof Explorer

Theorem rpne0

Description: A positive real is nonzero. (Contributed by NM, 18-Jul-2008)

		Ref	Expression
	Assertion	rpne0	$⊢ A \in ℝ^{+} \to A \neq 0$

Step	Hyp	Ref	Expression
1		rpregt0	$⊢ A \in ℝ^{+} \to (A \in ℝ \land 0 < A)$
2		gt0ne0	$⊢ (A \in ℝ \land 0 < A) \to A \neq 0$
3	1 2	syl	$⊢ A \in ℝ^{+} \to A \neq 0$