Am I assuming too much in this Natural Deduction proof? So I need to prove the following using natural deduction:
$M \to J, A \to J, \lnot M \to A, A \to \lnot J \vdash M, J, \lnot A$
This is my proof so far:
1.) $M \to J$
2.) $A \to J$
3.) $\lnot M \to A$
4.) $A \to \lnot J$
5.) $(M \to J) \lor (A \to J)  ----(\lor I 1,2)$
6.) $M ---- (\lor E 1,2,5)$ <- M is proven
7.) $J ---- (\lor E 1,2,5)$ <- J is proven
....(not sure how to prove $\lnot A$ yet)
So my question is, am I assuming to much? Am I doing this completely wrong? If so, where exactly am I assuming to much and do you have any hints or tips to lead me in the right direction? It seemed way to easy to prove M and J so it makes me think I'm jumping to conclusions.

From :
2) $A→J$
and
4) $A→¬J$
assuming : [a] $A$
we get $J$ and $\lnot J$ and thus, by $\land$-I, a contradiction :

$J \land \lnot J$.

Thus, by  $\lnot$-E followed by $\lnot$-I we derive :


$\lnot A$


discharging [a].
