Theorem rpre

Description: A positive real is a real. (Contributed by NM, 27-Oct-2007) (Proof shortened by Steven Nguyen, 8-Oct-2022)

	Ref	Expression
Assertion	rpre	⊢ ( 𝐴 ∈ ℝ+ → 𝐴 ∈ ℝ )

Proof

Step	Hyp	Ref	Expression
1		rpssre	⊢ ℝ+ ⊆ ℝ
2	1	sseli	⊢ ( 𝐴 ∈ ℝ+ → 𝐴 ∈ ℝ )