  The classical definition of {\em global hyperbolicity} for a spacetime
$(M,g)$ comprises two conditions: (A) compactness of the diamonds $J^+(p)\cap
J^-(q)$, and (B) strong causality. Here we show that condition (B) can be
replaced just by causality. In fact, we show first that the classical
definition of causal simplicity (which impose to be distinguishing, apart from
the closedness of $J^+(p)$, $J^-(q)$) can be weakened in causal instead of
distinguishing. So, the full consistency of the causal ladder (recently proved
by the authors in a definitive way) yields directly the result.
