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Metamath Proof Explorer

Theorem rpne0d

Description: A positive real is nonzero. (Contributed by Mario Carneiro, 28-May-2016)

		Ref	Expression
	Hypothesis	rpred.1	$⊢ φ \to A \in ℝ^{+}$
	Assertion	rpne0d	$⊢ φ \to A \neq 0$

Step	Hyp	Ref	Expression
1		rpred.1	$⊢ φ \to A \in ℝ^{+}$
2		rpne0	$⊢ A \in ℝ^{+} \to A \neq 0$
3	1 2	syl	$⊢ φ \to A \neq 0$