An indirect proof establishes a statement by proving a logically equivalent statement or by showing that its negation leads to a contradiction. The term includes two related but distinct methods.
To prove 
by contrapositive, one proves 
instead. These two implications are logically
equivalent, and the inference is an application of modus
tollens. In a proof by contradiction,
one assumes the negation of the statement to be proved
and derives a contradiction. Thus proof by contrapositive
and proof by contradiction are both indirect,
but they are not synonyms.
For example, to prove indirectly that if 
is even then the integer 
is even,
prove the contrapositive: if 
is odd, then 
for some integer 
, so 
is odd.
