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"an indispensable condition," Latin, literally "without which not," from sine "without" (see sans) + qua ablative fem. singular of qui "which" (see who) + non "not" (see non-). Feminine to agree with implied causa. The Latin phrase is common in Scholastic use. Sometimes a masculine form, sine quo non, is used when a person is intended. Proper plural is sine quibus non.
The essential, crucial, or indispensable ingredient without which something would be impossible: “Her leadership was the sine qua non of the organization's success.” From Latin, meaning “without which nothing.”