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 I have not pinpointed it, yet.

Maybe the quantifier foreach(P) in the second order predicate logic is too much strong.
I don't know. Philosophy of logic must answer.