Theorem rpcnne0

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

	Ref	Expression
Assertion	rpcnne0	$$⊢A\in {ℝ}^{+}\to \left(A\in ℂ\wedge A\ne 0\right)$$

Proof

Step	Hyp	Ref	Expression
1		rpcn	$$⊢A\in {ℝ}^{+}\to A\in ℂ$$
2		rpne0	$$⊢A\in {ℝ}^{+}\to A\ne 0$$
3	1 2	jca	$$⊢A\in {ℝ}^{+}\to \left(A\in ℂ\wedge A\ne 0\right)$$