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