The Latin original of this saying dates back over two millennia to Cicero. It means if you make an exception to a rule, a rule must exist. If you say “in case of fire students may use the emergency exits” it is clear that the rule is that normally students are not supposed to use those exits. Few people understand this point and they misuse the phrase “the exception proves the rule” to mean that a rule is not really a rule unless there is an exception to it. This makes no sense. It’s better to simply avoid this misleading phrase.
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