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Metamath Proof Explorer

Theorem rpcnd

Description: A positive real is a complex number. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypothesis rpred.1 ⊢ ( 𝜑 → 𝐴 ∈ ℝ+ )
Assertion rpcnd ( 𝜑 → 𝐴 ∈ ℂ )

Proof

Step Hyp Ref Expression
1 rpred.1 ⊢ ( 𝜑 → 𝐴 ∈ ℝ+ )
2 1 rpred ⊢ ( 𝜑 → 𝐴 ∈ ℝ )
3 2 recnd ⊢ ( 𝜑 → 𝐴 ∈ ℂ )