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Is there a Latin phrase that would be used when accepting some statement without providing the proof of such a statement?

For example, say you are working on an elementary number theory proof, and you make the statement "since $p$ is odd, $p^2$ is odd, which we accept [Latin phrase for 'without showing proof']." Obviously this is a simple thing to prove, but in some cases it might be nice to acknowledge that a proof exists and we do not wish to show it.

Could ex facie be used in such a situation ("we accept ex facie that $q$ odd implies $q^2$ odd")? Or failing the existence of a Latin phrase, is there a way that sounds a little less crude than "without proof"?

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    "manifestly". [It's quite latin](https://en.wiktionary.org/wiki/manifest#English).2016-07-22

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It appears as though ex facie bears the intended meaning. Prima facie has a similar meaning.

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Arguendo is close, and might better fit proofs by contradiction, or derivations from a conjecture.

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Are you thinking of a priori?

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    @DennisGulko look at the poster's reputation, it takes 50 reputation to post comments.2013-12-10
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Axiom (something that is accepted without proof) ex.: this statement is an Axiom.
Axiomatic, ex.: this statement is axiomatic in every sense.
Axiomatically, ex.: this statement is axiomatically accepted by some.
Note: Of Greek origin but surely used in Latin as well.