Natural deduction: given premises, conclude $M \lor E$.

Question

I need to prove that the following argument is valid using Natural Deduction:

1.  $[\lnot (B \lor \lnot I) \rightarrow (\lnot L \land J)]$

2.  $[\lnot L \rightarrow (M \land B)]$

3.  $\lnot (B \lor \lnot I)$ 

$\therefore \quad    (M \lor E)$

I'm very new to this, so I'd appreciate very much if someone can help me though the process. What's listed above are the premises, from which I need to determine if they validly lead to the conclusion at the bottom.  

Answer 1

From $(1)$ and $(3)$, by modus ponens (aka $\rightarrow$-elimination), infer

$(4)\quad \lnot L \land J$.

From $(4)$ infer

$(5) \quad \lnot L,\;$ by $\land$-elimination.

From $(2)$ and $(5)$, by modus ponens (aka $\rightarrow$-elimination) infer

$(6)\quad M\land B$.

$(7)\quad M,\;$ using $(6)$ and $\land$-elimination.

$\therefore\quad M \lor E,\;$ from $(7)$ and $\lor$-Introduction.

Answer 2

What does $E$ mean? Other then that we have:

$\neg L \wedge J$ (using $\rightarrow$E on 3. and 1.)

$\neg L$ (using $\wedge E$)

$M \wedge B$ (using $\rightarrow$E on 2.)

$M$ (using $\wedge$E)

$M \vee E$ (using $\vee$I)