1
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Phrase(s): without batting an eye
Lit. Fig. without showing alarm or response; without blinking an eye. • I knew I had insulted her, and she turned to me and asked me to leave without batting an eye. • Right in the middle of the speech—without batting an eye—the speaker walked off the stage.
McGrawhill's American Idioms And Phrasal Verbs
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Showing no emotion, acting as though nothing were unusual. For example, Richard ate the snails without batting an eye. A related phrase is not bat an eye, as in He didn't bat an eye when she told him he was being laid off. These expressions, which use bat in the sense of "blink," date from about 1900.
American Heritage Idioms