I think I realised my mistake. What I actually proved was
as was pointed out by makarov. I was confused by the consequent
part. Lets put it separately.
for the purpose of brevity. so above implication is
so when , and if we let
then both antecedent and consequent are
TRUE and all is well. But in other case when and if we let then antecedent is FALSE but consequent is TRUE . Though
in both case the implication itself is TRUE. I think that was the
source of confusion.