WTF definition
(a≤b) == foreach(ℙ) if ℙ(a) then ℙ(b)

WTF theorem
for any objects a and b we have:
if (a≤b) then (a=b)
Proof
since (a≤b) we have
foreach(ℙ) if ℙ(a) then ℙ(b)
Now if we take ℙ(t) as (a=t) then we have
if (a=a) then (a=b)
since always (a=a) 
hence (a=b)
QED/WTF


There must be a flaw in this proof, but and only but, there is not.

The quantifier foreach(ℙ) in the second order predicate logic, is too much strong.