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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Prime numbers and composite numbers are not used in daily jobs. However they are used by scientists to prove theorems.
Riders, lemmas, theorems.
No, because postulates are assumptions. Some true, some not. Proving a Theorem requires facts in a logical order to do so.
A proof uses postulates and theorems to prove some statement.
1.experiments.2.opinions.3.postulates.4.theorems.