  Non-perturbative results in QCD-like theories can be derived employing
positivity of the Euclidean path integral measure, as pioneered by Weingarten,
Vafa, Witten. We show that positivity of the measure can be generalized to
parity-invariant theories with Yukawa couplings to fundamental scalars,
provided the fermions are Dirac and carry a real representation of the gauge
group. This result allows us to demonstrate the conservation of parity and
vector-like flavor symmetries in such theories, as well as to derive exact
inequalities among hadrons' masses.
