theorem :: BORSUK_6:76

for X being non empty pathwise_connected TopSpace
for a1, b1, c1 being Point of X
for P1, P2 being Path of a1,b1
for Q1, Q2 being Path of b1,c1 st P1,P2 are_homotopic & Q1,Q2 are_homotopic holds
P1 + Q1,P2 + Q2 are_homotopic