From this property, we can conclude that the effective impulse response of a cascaded LTI system is given by the convolution of their individual impulse responses.

       

Consequently the unit impulse response of a cascaded  LTI  system is independent of the order in which the individual  LTI  systems are connected.

 Note : All the above three properties are certainly obeyed by  LTI  systems, but may / may not hold for non-LTI systems in, as seen from the following example: