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Metamath Proof Explorer

Theorem rpxr

Description: A positive real is an extended real. (Contributed by Mario Carneiro, 21-Aug-2015)

Ref Expression
Assertion rpxr ( 𝐴 ∈ ℝ+ → 𝐴 ∈ ℝ* )

Proof

Step Hyp Ref Expression
1 rpre ⊢ ( 𝐴 ∈ ℝ+ → 𝐴 ∈ ℝ )
2 1 rexrd ⊢ ( 𝐴 ∈ ℝ+ → 𝐴 ∈ ℝ* )