It is common in mathematics to prove a theorem p by assuming it
is false and deriving a contradiction, i.e., derive false
or something equivalent to false, like 
. The justification for this
proof technique is the following property about implication, repeated
from Section 2:
By substituting 
for p and using double negation, we derive
the theorem:
(Proof by Contradiction)
Hence, having proved that 
is a
theorem,
you may conclude that p is a theorem.