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Phrase(s): not bat an eyelid [and] not bat an eye
Fig. to show no signs of distress even when something bad happens or something shocking is said. • Sam didn’t bat an eyelid when the mechanic told him how much the car repairs would cost. • The pain of the broken arm must have hurt Sally terribly, but she did not bat an eyelid.
McGrawhill's American Idioms And Phrasal Verbs