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 )