Theorem rpabsid

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

	Ref	Expression
Assertion	rpabsid	⊢ ( 𝑅 ∈ ℝ+ → ( abs ‘ 𝑅 ) = 𝑅 )

Proof

Step	Hyp	Ref	Expression
1		rpre	⊢ ( 𝑅 ∈ ℝ+ → 𝑅 ∈ ℝ )
2		rpge0	⊢ ( 𝑅 ∈ ℝ+ → 0 ≤ 𝑅 )
3		absid	⊢ ( ( 𝑅 ∈ ℝ ∧ 0 ≤ 𝑅 ) → ( abs ‘ 𝑅 ) = 𝑅 )
4	1 2 3	syl2anc	⊢ ( 𝑅 ∈ ℝ+ → ( abs ‘ 𝑅 ) = 𝑅 )