Theorem rpcnne0

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

	Ref	Expression
Assertion	rpcnne0	⊢ ( 𝐴 ∈ ℝ+ → ( 𝐴 ∈ ℂ ∧ 𝐴 ≠ 0 ) )

Proof

Step	Hyp	Ref	Expression
1		rpcn	⊢ ( 𝐴 ∈ ℝ+ → 𝐴 ∈ ℂ )
2		rpne0	⊢ ( 𝐴 ∈ ℝ+ → 𝐴 ≠ 0 )
3	1 2	jca	⊢ ( 𝐴 ∈ ℝ+ → ( 𝐴 ∈ ℂ ∧ 𝐴 ≠ 0 ) )