Prove that $p(rp)$ is a tautology.

$p(rp)-=p(notrvvp)$

$-=$notpvv$(notrvvp)$

$-=$notpvv$(pvvnotr)$

$-=(notpvvp)vvnotr$

$-=(pvvnotp)vvnotr$

$-=$Tvvnotr

$-=$notrvvT

$-=T$

Idempotent law

Associative law

Commutative law

Distributive law

Identity law

Domination law

Double negation law