Не сегодня, но и не завтра

Is it really necessary to put the "но"?
For one I don't think it changes what you're trying to say, and also leaving the "но" out, to me, sounds better and is easier to say...
But, please enlighten me if it's necessary, sounds more formal or has some other reason for existing in this sentence...

@DasCapschen As I understand it:
Не сегодня, и не завтра - Not today, and not tomorrow
Не сегодня, но и не завтра - Not today, but also not tomorrow
You might use the second version, I think, if there was an assumption that 'if not today, then tomorrow', and you wanted to strongly contradict this.

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