Simplifying a logical equivalence statement without a truth table

[needshelp5]

Homework Statement

[(p->r) ^ (q->r)] -> (p ^ q) -> r

Homework Equations

anything but a truth table! laws such as (p->q)= ~(p^~q) or (p->q)=(~q->~p) might help

 

[Mark44]

See how far you get using the relevant equations you showed. Other relevant equations that will come in handy are DeMorgan's Laws, ~(p ^ q) <==> ~p V ~q, and ~(p V q) <==> ~p ^ ~q.