  In the theory of conditional sets, many classical theorems from areas such as
functional analysis, probability theory or measure theory are lifted to a
conditional framework, often to be applied in areas such as mathematical
economics or optimization. The frequent experience that such theorems can be
proved by `conditionalizations' of the classical proofs suggests that a general
transfer principle is in the background, and that formulating and proving such
a transfer principle would yield a wealth of useful further conditional
versions of classical results, in addition to providing a uniform approach to
the results already known. In this paper, we formulate and prove such a
transfer principle based on second-order arithmetic, which, by the results of
reverse mathematics, suffices for the bulk of classical mathematics, including
real analysis, measure theory and countable algebra, and excluding only more
remote realms like category theory, set-theoretical topology or uncountable set
theory, see e.g. the introduction of \cite{simpson2009subsystems}.This transfer
principle is then employed to give short and easy proofs of conditional
versions of central results in various areas of mathematics, including theorems
which have not been proven by hand previously such as Peano existence theorem,
Urysohn's lemma and the Markov-Kakutani fixed point theorem. Moreover, we
compare the interpretation of certain structures in a conditional model with
their meaning in a standard model.
