Consider k boxes where k is a positive integer, and suppose we need to put k+1 balls into k boxes. To prove: there is a box that contains two or more balls. QED To use the proof by contradiction, we assume that we can put k+1 balls into k boxes such that no box contains 2 or more balls. The statement to be proved is an existentially quantified statement. The assumption is not true and there must be a box that contains at least 2 balls. Proof The above statement is contradicting to the statement that we can put k+1 balls into k boxes. Since there are k boxes and each box contains at most 1 ball, we can put at most k balls into these k boxes