Deductive reasoning uses the law of logic to link together true statements to arrive at conclusion. Definition is true statement, so it is used in proof. a proof is valid argument that establishes the truth of a statement.

direct proof is proof that start with the given statement that use the law of logic to arrive at the statement to be proved.
indirect proof or proof by contradiction is proof that starts with the negation of the statement to be proved and use the law of logic to show that it is false. when the negation of statement is false, the statement must be true, if we can show that the negation of the statement to be proved is false, then the statement must be true.