This paper concerns the existence of a solution to the differential inclusion with constraint \[ u'(t)\in F(t,u(t)),\quad u(t)\in D(t). \] This problem -- already well-known in finite-dimensional space -- is here studied in an abstract separable space. The viability theorem is proved for weakly upper semicontinuous weakly compact and convex valued right-hand side for a tube of constraints which is left-upper semicontinuous and locally strongly compact valued.