If my penmanship is undecipherable, here is what was meant to be said (taken down in a symbolic logic class):
"Suppose that χ⊢(ɸ -> Ψ), then it is possible for χ to be true and (ɸ -> Ψ) false. So it must be possible for ɸ to be true and Ψ to be false.
For ⊢(ɸ -> (χ -> Ψ)), ɸ and (χ -> Ψ) must be both true or ɸ must be false. If you find a contradiction, then it is valid. If you don't, then it is invalid."
I screwed up the "you don't" part -- it looks like I wrote "one don't or undone" and my FAI for "find" looks like SAI, but I read it back to myself so whateva.
(by Stan for group greggshorthand)
