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Metamath Proof Explorer

Theorem rpabsid

Description: A positive real is its own absolute value. (Contributed by SN, 1-Oct-2025)

		Ref	Expression
	Assertion	rpabsid	$⊢ R \in ℝ^{+} \to \|R\| = R$

Step	Hyp	Ref	Expression
1		rpre	$⊢ R \in ℝ^{+} \to R \in ℝ$
2		rpge0	$⊢ R \in ℝ^{+} \to 0 \leq R$
3		absid	$⊢ (R \in ℝ \land 0 \leq R) \to \|R\| = R$
4	1 2 3	syl2anc	$⊢ R \in ℝ^{+} \to \|R\| = R$