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Metamath Proof Explorer

Theorem rprege0

Description: A positive real is a nonnegative real number. (Contributed by Mario Carneiro, 31-Jan-2014)

		Ref	Expression
	Assertion	rprege0	$⊢ A \in ℝ^{+} \to (A \in ℝ \land 0 \leq A)$

Step	Hyp	Ref	Expression
1		rpre	$⊢ A \in ℝ^{+} \to A \in ℝ$
2		rpge0	$⊢ A \in ℝ^{+} \to 0 \leq A$
3	1 2	jca	$⊢ A \in ℝ^{+} \to (A \in ℝ \land 0 \leq A)$