  We know extensions of first order logic by quantifiers of the kind "there are
uncountable many ...", "most ..." with new axioms and appropriate semantics.
Related are operations such as "set of x, such that ...", Hilbert's
$\epsilon$-operator, Churche's $\lambda$-notation, minimization and similar
ones, which also bind a variable within some expression, the meaning of which
is however partly defined by a translation into the language of first order
logic. In this paper a generalization is presented that comprises arbitrary
variable-binding symbols as non-logical operations. The axiomatic extension is
determined by new equality-axioms; models assign functionals to
variable-binding symbols. The completeness of this system of the so called
"Functional Logic of 1st Order" will be proved.
