Natural deduction proof of $(c ∧ n) → t, h ∧ ¬s, h ∧ ¬(s ∨ c) → p \vdash (n ∧ ¬t) → p$ I'm trying to do a question from Huth and Ryan's book Logic in Computer Science and I am stuck on the following natural deduction proof: 
Prove by natural deduction that the sequent 
$$(c ∧ n) → t, h ∧ ¬s, h ∧ ¬(s ∨ c) → p \vdash (n ∧ ¬t) → p$$ 
is valid.
I have tried assuming $n ∧ ¬t$ on line 4 after the premises, and using Modus Tollens from there to get $¬(c ∧ n)$, but I don't know what I can do after that. Any help would be appreciated. 
 A: $\begin{align}n, \neg (c\wedge n)\vdash&~ \neg c \\ h\wedge \neg s\vdash&~ \neg s \\ h\wedge \neg s\vdash&~ h \\ \neg c, \neg s\vdash&~ \neg (s\vee c)\\ h, \neg(s\vee c), h\wedge \neg (s\vee c)\to p\vdash & ~ p\end{align}$
More or less.  Format and provide justifications .
A: Here's a proof that might help:

Here is the OP's attempt:

I have tried assuming n∧¬t on line 4 after the premises, and using Modus Tollens from there to get $¬(c∧n)$, but I don't know what I can do after that. 

The OP reached line 6 of this proof. 
After that I used De Morgan's rules (DeM) on line 7. However, doing that left me with a disjunction. I considered the two cases of the disjunction on lines 10-14 and 15-18. They both led to $P$ which allowed me to use disjunction elimination (vE) on line 19. Line 20 used a conditional introduction to conclude the proof.
For more information about these rules or to try the proof checker see the links below.

Kevin Klement's JavaScript/PHP Fitch-style natural deduction proof editor and checker http://proofs.openlogicproject.org/
P. D. Magnus, Tim Button with additions by J. Robert Loftis remixed and revised by Aaron Thomas-Bolduc, Richard Zach, forallx Calgary Remix: An Introduction to Formal Logic, Winter 2018. http://forallx.openlogicproject.org/
