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Yes, they can. This is done all the time in mathematics, logic and other areas. However, you must ensure that you either record the theorems used, or write them out in whole and attach them to the proof of the new theorem.

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Q: Can theorems be used to prove other theorems?
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Related questions

What is used to the steps of a geometric proof?

we use various theorems and laws to prove certain geometric statements are true


How are prime and composite numbers used in everyday jobs?

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The axiomatic structure of geometry, as initiated by Euclid and then developed by other mathematicians starts of with 8 axioms or postulates which are self-evident truths". Chains of logical reasoning can be used to prove theorems which are then accepted as additional truths, and so on. Geometry does not have laws, as such.


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