$$p\Rightarrow (p\Leftrightarrow q)$$
$$\equiv$$
$$p'\vee [(p\Rightarrow q)\wedge (q\Rightarrow p)]$$
$$\equiv$$
$$p'\vee [(p'\vee q)\wedge (q'\vee p)]$$
$$\equiv$$
$$[p'\vee (p'\vee q)]\wedge\underset{1}{\underbrace{[p'\vee (q'\vee p)]}} $$
$$\equiv$$
$$[p'\vee (p'\vee q)]\wedge 1$$
$$\equiv$$
$$p'\vee (p'\vee q)$$
$$\equiv$$
$$(p'\vee p')\vee q$$
$$\equiv$$
$$p'\vee q$$
$$\equiv$$
$$p\Rightarrow q$$