Can anyone help me with this basic derivation with natural rules of inference: $$ Q \rightarrow R \vdash (P \rightarrow Q) \rightarrow (P \rightarrow R) $$ I can use the follwing: $\wedge I, \wedge E, \vee I, \vee E, \rightarrow I, \rightarrow E, \leftrightarrow I, \leftrightarrow E, RAA $
I am struggling to understand where to go from assumption of line 2:
$$ 1. Q \rightarrow R \qquad\qquad\qquad given $$
$$ \qquad 2. P \rightarrow Q \qquad\qquad\quad assume $$ $$ \qquad 3. P \rightarrow R \qquad\qquad \rightarrow E $$
$$ Get: (P \rightarrow Q) \rightarrow (P \rightarrow R) $$
Am I going the right direction? I wanted to introduce another arrow elimination to get Q, R and P but I'm not too sure if that's correct.
My apologies for such a silly question - I'm only the beginner.