Original: The one major exception to this in practice is the axiom of choice - unless studying this axiom in particular, the majority of researchers do not usually worry whether a result requires the axiom of choice.
Simplified: In this case, if a proof uses this statement, researchers will often look for a new proof that does not require the hypothesis The one major exception to this in practice is the axiom of choice - unless studying this axiom in particular, the majority of researchers do not usually worry whether a result requires the axiom of choice.