Anyone good with proposition logics? that can help out?

im stuck on one question and can't figure out the next step.

The question states : Use the rules of inference to prove the following.

(p -> q) ^ (r -> s) ^ [t -> ~(q V s) ^ t => (~p ^ ~r)

note : the " ~ " sign means NOT,

the " ^ " sign means AND,

the " -> " sign means implies/conditional

the " V " sign means OR

the " => " sign means resultant or conclusion is.

I've set up my working up to look like this.

P -> q H1(Hypothesis 1)

r -> s H2(Hypothesis 2)

t -> ~(q V s) H3(Hypothesis 3)

t H4(Hypothesis 4)

_____________

~p ^ ~r C (Conclusion)

Step one. I got H4 with H3 and AND both of them >> H4 ^ H3 which gives:

t ^ [t -> ~(q V s)] and since t ^ t cancels out with the modus ponens rules it leaves us with ~(q V s).

So now that H4 and H3 is gone we have H1 and H2 left. This is where i got stuck.

I decided to use de morgan's law to simplify which gave me >> ~(q V s) => ~q ^ ~s and we can call this theory one (1).

So far i've only got up to this part and now i'm stuck could you help me figured out what i need to do next?

Working : t ^ [t -> ~(q V s)] <=> ~(q V s) H4 ^ H3

<=> ~q ^ ~s (1).

Next step = ? please help