Conditional Elimination

It looks like this:

What does it mean?

It means that if you have both a conditional, P-->Q, and its antecedent, P, then you are entitled to claim its consequent, Q.

The authors of LPL call this rule "conditional elimination." Many textbooks contain roughly the same rule and call it "Modus Ponens."

(I think that's Latin.)

Generally, any argument of the form

is a valid argument. Philosophers and logicians will say that such arguments have the form of modus ponens.