Do I have to have songs downloaded to iTunes to have them on my iPhone?

I have limited space on my macbook air, so to save room could I delete my songs from my actual computer and sync them from the cloud, while still being able to access them from iCloud in iTunes on my mac? Or must the songs be downloaded onto my mac to sync to my iPhone 5?

You can delete then from both iCloud and iTunes after the songs are on the device

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