$$\require{AMScd}
\begin{CD}
\pi_{1}(X,x_0) @>(h_{x_{0}})_{\bullet}>> \pi_{1}(Y,y_0)\\
@VV\hat{\alpha}V @VV\hat{\beta}V\\
\pi_{1}(X,x_1) @>(h_{x_{1}})_{\bullet}>> \pi_{1}(Y,y_1)\\
\end{CD}$$.
I have to show that the following diagram commutes . Given that $h:X\to Y$ such that $h(x_0)=y_0, h(x_1)=y_1$.
Any hints on how should I prove this?