The Free On-line Dictionary of Computing (30 December 2018):

implies
implication
imply

    (=> or a thin right arrow) A binary Boolean function
   and logical connective.  A => B is a true implication unless
   A is true and B is false.  The truth table is

   	A B | A => B
   	----+-------
   	F F |   T
   	F T |   T
   	T F |   F
   	T T |   T

   It is surprising at first that A => B is always true if A is
   false, but if X => Y then we would expect that (X & Z) => Y
   for any Z.

   If A is actually an expression X & Y then the implication is
   called a syllogism.

   (2009-10-28)