cardboard adolescent

let me set it up less ambiguously (because i don't get what you're saying)

a = b (or, a is b is true)
b = ~a (or, b is a is false)
the question is, a->b? (does a give you b?)
if yes, a -> b and so through substitution a->~a, which is contradictory
if no, a -> ~b, substituting a this time you get b->~b, which is also contradictory

a simpler expression of the same paradox would simply be:

this statement is false