sine qua non

[sahy-nee kwey non, kwah, sin-ey; Latin si-ne kwah-nohn]
noun
an indispensable condition, element, or factor; something essential: Her presence was the sine qua non of every social event.

Origin:
< Late Latin sine quā (causā) nōn without which (thing) not

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Based on the Random House Dictionary, © Random House, Inc. 2014.
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Collins
World English Dictionary
sine qua non (ˈsaɪnɪ kweɪ ˈnɒn)
 
n
an essential condition or requirement
 
[literally: without which not]

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Etymonline
Word Origin & History

sine qua non
"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.
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Cultural Dictionary
sine qua non [(sin-i kwah non, nohn)]

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.”

The American Heritage® New Dictionary of Cultural Literacy, Third Edition
Copyright © 2005 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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American Heritage
Idioms & Phrases

sine qua non

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.

The American Heritage® Dictionary of Idioms by Christine Ammer.
Copyright © 1997. Published by Houghton Mifflin.
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Example sentences
Nevertheless, in a free society the right to pursue one's own notions of
  happiness is a sine qua non.
The hung parliament, a sine qua non, did in fact happen.
But voters' ability to throw the rascals out at regular intervals is still the
  indispensable sine qua non.
Both are sine qua non for citizens to have a decent standard of living and
  avoid the squalor of poverty.
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