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| mat·ter of fact |
noun |
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1. actual fact: something that is true and that cannot be denied
 It's a matter of fact that our scores improved.
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2. something to be proved or disproved: a question to be decided by a court of law that involves deciding on the truth of a statement, rather than interpreting a point of law or forming an opinion.
See also matter of law
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as a matter of fact
1. used to add a statement that completes what you are saying or emphasizes its truth
2. used to contradict what somebody else has said or to express disagreement
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