C# Webclient Stream download file from FTP to local storage

I've been downloading files from an FTP server via the WebClient object that the .NET namespace provides and then write the bytes to a actual file via a BinaryWriter. All is good. However, now, the files have dramatically increased in size and I'm worried about memory constraints so I'd like to create a download stream, create an file stream, and line by line read from the download and write to the file.

I'm nervous since I couldn't find a nice example of this. Here's my end result:

var request = new WebClient();

// Omitted code to add credentials, etc..

var downloadStream = new StreamReader(request.OpenRead(ftpFilePathUri.ToString()));
using (var writeStream = File.Open(toLocation, FileMode.CreateNew))
{
    using (var writer = new StreamWriter(writeStream))
    {
        while (!downloadStream.EndOfStream)
        {
            writer.Write(downloadStream.ReadLine());                  
        }
    }
}

Am I going about this incorrect/better way/etc?