"an indispensible condition," c.1600, from L., lit. "without which not," from sine "without" + qua ablative fem. sing. of qui "which" + non "not." Fem. to agree with implied causa. The L. phrase is common in Scholastic use. Sometimes a masc. 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.”
An essential element or condition, as in A perfect cake is the since qua non of a birthday party. This phrase is Latin for “without which not” and has been used in English since about 1600. It appears more in writing than in speech.