  In this brief article an internal symmetry of a generic metric compatible
space-time connection, metric and generalized volume element is introduced. The
symmetry arises naturally by considering a space-time connection containing a
generic torsion tensor, and would otherwise be missed in the absence of
torsion. When the transformation is applied to the Hilbert-Einstein action it
is shown that by a choice of gauge all possible field theories arising from the
Hilbert-Einstein action are equivalent to the standard theory of gravity
described by general relativity.
