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Where in Shas can I find the statement that with every chumra one takes on, he is in essence going to be taking a on a kula somewhere else? I'm pretty sure it's in Beitza somewhere...

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The gemara does not say that every stringency leads to a leniency, but sometimes it does, and thus the gemara may challenge that a certain stringency is a חומרא דאתי לידי קולא - a stringency which leads to a leniency, for example in Pesachim 48b, Yevamos 30b, Bava Kama 11a and Niddah 24b.

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How do you know it never says that? – Double AA Mar 6 '14 at 22:20
@DoubleAA wouldn't finding any chumra not challenged thusly be how one would know? If that is a challenge to a chumra, and every chumra leads to a kula, then it would be a challenge to every chumra. – Y ez Mar 7 '14 at 3:42
it doesnt have to be a challenge to be a rule so your sylogism fails @yez – Double AA Mar 7 '14 at 4:01
@DoubleAA Any suggestion for why it would be a bothersome point for a chumra to lead to a kula some days but not others? – Y ez Mar 7 '14 at 4:10
@YEZ It's not a matter of what day it is. It matters how big the kula is. I don't know where I implied that its temporally linked. – Double AA Mar 7 '14 at 4:12

The closest thing I could find is this, on 16a:

ואמר רב תחלת הוראה דהאי צורבא מרבנן לקלקולא אי אמרת בשלמא לקולא קאמר היינו קלקולא אלא אי אמרת לחומרא מאי קלקולא איכא כיון דמקלקלי בה רבים היינו קלקולא
(in the context of a chumra) Rav Tachlis says: This young rabbi's ruling is problematic. The gemara asks "if it were unnecessarily lenient I would understand why that's a problem, but it's stringent, so what could go wrong? [Answer] Because people will violate it (due to its stringency) that is a problem in and of itself. (my translation)

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