A direct proof is a proof method by applying established facts, such as axioms and existing lemmas and theorems without further assumptions. 1

Logic

In logic, a direct proof means applying 2

  1. premise
  2. an instance of an axiom schemas
  3. an rule of inference

Here is an example, given modus ponens, and three promise , , and , we can prove by first writing down premises and repletely applying the inference rule as following 2:

  1. (premise)
  2. (premise)
  3. (premise)
  4. (modus ponens: 1, 2)
  5. (modus ponens: 2, 3)
  6. (modus ponens: 4, 5)

Footnotes

  1. Direct proof - Wikipedia

  2. Introduction to Logic - Chapter 4 2