So I've been given one question from my colleague, which needs to prove using below premises in order to draw a certain conclusion (see hypothesis below).
I've been doing this from last night and by out of luck, I can't get the hypothesis right, even by referring to Wikipedia rules table here.
Premise 1: $(\neg P \rightarrow Q) \rightarrow R$
Premise 2: $P \rightarrow R$
Premise 3: $Q \rightarrow R$
Hypothesis: $Q \rightarrow (P \rightarrow R)$
From my observation, by using the first premise, I can draw out the second and third premises, but then I getting stuck there.
1) $(\neg P \rightarrow Q) \rightarrow R$
2) $\neg(\neg P \rightarrow Q) \vee R$
3) $\neg (\neg \neg P \vee Q) \vee R$
4) $\neg (P \vee Q) \vee R$
5) $(\neg P \wedge \neg Q) \vee R$
6) $(\neg P \vee R ) \wedge (\neg Q \vee R)$
7) $(P \rightarrow R ) \wedge (Q \rightarrow R)$
Can somebody point out what steps should I do in order to draw the hypothesis conclusion from above three premises?