In nonstandard analysis, the transfer principle is the technical form of the following intuitive idea: "Anything provable about
a given superstructure 
by passing to a nonstandard enlargement 
of 
is also provable without doing so, and vice versa." It
is a result of Łoś' theorem and the completeness
theorem for first-order predicate logic
The transfer principle is stated as follows. Let 
be a superstructure, let 
be an enlargement of 
, let 
be any sentence in the language for 
, and let 
denote the 
-transform of 
. Then 
if and only if 
.
