P⇔QP \Leftrightarrow QP⇔Q means P⇒QP \Rightarrow QP⇒Q and Q⇒PQ \Rightarrow PQ⇒P. To prove it, prove both directions.
(⇒)(\Rightarrow )(⇒) Assume PPP and show QQQ. (⇐)(\Leftarrow )(⇐) Assume QQQ and show PPP.