Hello guys!!I am from Greece so sorry for my bad english...

I have a problem at propositional logic...specifically at the proofing system...

the excercise which made me crazy is the following...

proove : $\displaystyle \vdash ((\phi \rightarrow{\psi})\rightarrow{\neg{\chi}})\rightar row{(\chi} \rightarrow{\neg{(\phi \rightarrow{\psi})}})

$

we can use the following axioms and theorems...

$\displaystyle \vdash ((\phi \rightarrow{(\psi \rightarrow{\sigma})})\rightarrow{((\phi \rightarrow{\psi})\rightarrow{(\phi \rightarrow \sigma})})$

$\displaystyle \vdash \phi \rightarrow{(\psi \rightarrow{\phi})}$

$\displaystyle \vdash(\neg{\phi} \rightarrow{\neg \psi} )\rightarrow{((\neg \phi \rightarrow{\psi})\rightarrow{\phi})}$

$\displaystyle \phi \rightarrow \psi \vdash \neg{\psi} \rightarrow \neg{\phi}$

$\displaystyle \vdash \phi \rightarrow \psi \equiv \phi \vdash \psi$

thanx for advance for your help...

if u know any good source to study about axiomatic system plz tell me thanx again...