Theorem rpcndif0

Description: A positive real number is a complex number not being 0. (Contributed by AV, 29-May-2020)

	Ref	Expression
Assertion	rpcndif0	$$⊢A\in {ℝ}^{+}\to A\in \left(ℂ\setminus \left\{0\right\}\right)$$

Proof

Step	Hyp	Ref	Expression
1		rpcnne0	$$⊢A\in {ℝ}^{+}\to \left(A\in ℂ\wedge A\ne 0\right)$$
2		eldifsn	$$⊢A\in \left(ℂ\setminus \left\{0\right\}\right)\leftrightarrow \left(A\in ℂ\wedge A\ne 0\right)$$
3	1 2	sylibr	$$⊢A\in {ℝ}^{+}\to A\in \left(ℂ\setminus \left\{0\right\}\right)$$