on condition that
conjunction
UK: /ɒn kənˈdɪʃən ðæt/
US: /ɑːn kənˈdɪʃən ðæt/
If something will only happen or be true if something else happens or is true.
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I will lend you the book on condition that you return it next week.
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The bank approved the loan on condition that we provide additional collateral.
Only if a particular thing happens or is done.
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We will sign the contract on condition that the price is right.
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The university accepted her application on condition that she pass the entrance exam.