Can you distribute implication statements? Logically, the following statement makes sense in my head, but I can't find a law or proof that gives this example or explains this.
$$ ((p \lor q) \to r) \;\;\text{is equivalent to}\;\; ((p \to r) \lor (q \to r)) $$
I would think this is sort of like the distributive property, but I cant find a law that allows this (or I keep skipping over it in my notes).

(Elaborating on the first two comments under the question.)

*

*$$(p \lor q) \to r$$ means “the truth of either of $p$ or $q$
guarantees the truth of $r$”, whereas $$(p \to r) \lor (q \to r) $$
means “both $p$ and $q$ must be true to guarantee $r$'s truth”
  (having only one of $p$ and $q$ true is insufficient to
guarantee $r$'s truth because its corresponding argument of the
disjunction might be false).

*$${\quad(p \lor q) \to r\\\equiv\lnot(p \lor q)\lor r\\\equiv(\lnot p\land\lnot q)\lor r\\\equiv (\lnot p\lor r) \land (\lnot q\lor r)\\\equiv (p \to r) \land (q \to r)\\~\\\quad(p\land q)\to r \\\equiv \lnot(p\land q)\lor r\\\equiv (\lnot p\lor\lnot q)\lor r\\\equiv (\lnot p\lor r)\lor(\lnot q\lor r)\\\equiv (p\to r)\lor(q\to r)}$$
