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Metamath Proof Explorer

Theorem rpred

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

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

Step	Hyp	Ref	Expression
1		rpred.1	$⊢ φ \to A \in ℝ^{+}$
2		rpssre	$⊢ ℝ^{+} \subseteq ℝ$
3	2 1	sselid	$⊢ φ \to A \in ℝ$