I am trying to prove the following is a tautology using boolean algebra. I have proved it is using a truth table. I have to state which rule is used at each step.

$\displaystyle (a \Rightarrow b) \vee a $

Below is my attempt, how's it look?

$\displaystyle (a \Rightarrow b) \vee a = (\neg a \vee b) \vee a, (Rewriting \Rightarrow) $

$\displaystyle = (\neg a \vee a) \vee b, (Associativing) $

$\displaystyle = T \vee b, (Negation (i)) $

$\displaystyle = T, (Absorbtion) $