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Metamath Proof Explorer

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 )