Be the First 1 (leave only the first Truthy)
Python 2, 35 bytes



while 1:b=input();print b;True&amp;=b&lt;1


Try it online! Input and output are lines of True/False.

Based on Dennis's solution. Redefines the variable True to be False after a True input is encountered. That way, any further inputs of True will evaluate to False and be printed as such. Python 3 no longer allows True and False to be redefined, so this answer uses Python 2.

The redefinition is True&amp;=b&lt;1, i.e. True = True &amp; (b&lt;1). When the input b is True, then (b&lt;1) is False (since True==1), so True becomes False. See Kevin Cruijssen's answer for a shorter way to handle this redefinition.