In this introduction to propositional logic we will be looking at only
two rules of inference for generating new theorems. These are as follows:
Modus Ponens (method of assertion) allows us to reduce an implication
to the right hand statement if the left hand statement can be shown
to be true. In other words if you have an expression in you list of
hypotheses and theorems that match the expression E -> F
and the expression E then you can add the theorem
F to you list.
Simplification allows us to reduce a logical and statement to
either of its components.
In other words if you have an expression in your list of hypotheses and
theorems that match the expression E and F then you
can add to your list the expression E.
Similarly you can add to your list of theorems the
expression F.
The following application of the above rules of inference lead us to
the desired proof: