What would be a reference for the following property of symmetric spaces?


Given a smooth curve $\gamma : [0,1] \rightarrow M$ on a symmetric space $(M,g)$, there exists an isometry $\varphi : M \rightarrow M$ taking $\gamma(0)$ to $\gamma(1)$ and such that the parallel transport map 
$$
P\_\gamma : T\_{\gamma(0)}M \longrightarrow T\_{\gamma(1)}M 
$$
equals the differential of $\varphi$ at the point $\gamma(0)$.


I guess one can get this from two particular cases: (1) the curve $\gamma$ is closed and we are looking at holonomy vs. isotropy groups, and (2) the curve $\gamma$ is a geodesic segment and is the projection of a translation of one-parameter subgroup of isometries, but I would love just to be able to cite something.


I looked up in Helgason and it does not seem to be there, at least in this guise. 



Parallel transport on Riemannian symmetric spaces
As for the reference see Kobayashi-Nomizu Vol I page 262 Corollary 7.6.


Besides Petrunin's well-known argument the claim is also an obvious corollary of Cartan's Theorem 2.1 page 157 of Do Carmo's "Riemannian Geometry"


