I am doing a practice exam and in it is the following question:
Show without truth tables that the following logical equivalence holds:
$$(p → q) ∧ (p → r) ≡ p → (q ∧ r)$$
I attempted to substitute the left side's $(p \rightarrow q)$ and then apply the distributive laws, but what I got as a result was terribly long and messy.
I found a sample proof over here. However that is a proof using the tableau method of natural deduction and we still haven't covered that in class.
Is there a simpler proof?