This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem rpcn

Description: A positive real is a complex number. (Contributed by NM, 11-Nov-2008)

Ref Expression
Assertion rpcn ( 𝐴 ∈ ℝ+ → 𝐴 ∈ ℂ )

Proof

Step Hyp Ref Expression
1 rpre ⊢ ( 𝐴 ∈ ℝ+ → 𝐴 ∈ ℝ )
2 1 recnd ⊢ ( 𝐴 ∈ ℝ+ → 𝐴 ∈ ℂ )