Suppose a theorem proposes If P then Q.
Are the only two ways to prove that the If-then statement is true is to show that for any P, Q must be the consequent?
I've heard that another way to prove that the statement is true is to show that for any ~Q, the consequent must be ~P. That is, if we show that If ~Q then ~P is true, then we can conclude If P then Q is true.
Disproving an If-then statement would be: Show that for at least one P, ~Q or for one ~Q, not ~P.
That all there is to this logic stuff :|?