Mesorat%20hashas for Sukkah 14:5

ואי אשמעינן הני תרתי מחמירתא לקילתא אבל מקילתא לחמירתא אימא לא צריכא:

And if we had been informed of both those laws [but not of the third,] one would have assumed that from the more stringent to the less stringent [we apply the rule of ‘since’] but not from the less stringent to the more. [Therefore all the three rules were] necessary.

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