Theorem 7.1:

If $\gamma_1,\; \gamma_2,\; \gamma_3$ are three paths in $X$ such that

$$\gamma_1(0)= \gamma_2(0) = \gamma_3(0)\;\; \;\; \gamma_1(1) = \gamma_2(1) = \gamma_3(1),$$

$\gamma_1$    and $\gamma_2$ are homotopic; $\gamma_2$    and $\gamma_3$ are homotopic then $\gamma_1$    and $\gamma_3$ are homotopic.