There is a rule in formal logic that goes like this:

if p or q, but not q, then p

but, of course, you have to have the letters stand for something, so lets have it so that

p stands for Gore is president and where q stands for Bush is president.

Therefore, if you insert these sentences it translates into the following:

If Gore is president or Bush is president, but Bush is not president, then Gore is president.

But, for a proof to be valid, you can’t have true premises that lead to a false conclusion, meaning that for the statement to be invalid it has to be true that either Gore or Bush is president, and that Bush is not president, but untrue that Gore is president. Any other combination of true and false values would make the proof valid.

Lets try another rule

If p then q, but not q, therefore not p

if we insert the same sentences as above it would result in the following:

If Gore is president, then Bush is president, but Bush is not president, therefore Gore is not president.

The form of this argument is valid, mainly because not all the premises are true. The amount of untrue statements in this proof is up to you, though, and either way it doesn’t change the fact that the proof is valid.

So, going by this logic, the following proof would be valid:

If p then q, but not q, then not p

where p is this is a poem and q is formal logic is poetry

when substituted it goes like this

If this is a poem, then formal logic is poetry

formal logic is not poetry

therefore this is not a poem.