\ is a set of sentences including the logically false sentence P.
(for contradiction) that \ is consistent.
by the definition of consistency, it is possible that all members of \ be true together.
P, a member of \, is possibly true. But that means that P is not logically false. However, we are supposing from the beginning that it is logically false!
our assumption (in red) leads to a contradiction. That assumption is wrong, so \ is inconsistent after all.
Suppose that      __________
Assume       __________
Then,      __________
So, it follows that      __________
Thus       __________

1.4ex III
More Informal Proofs

Matching. Drag sentences from the right to the correct location in the proof box. Don't print until you've come to the final page of this exercise.

First show that...

1. If some member of a set of sentences is logically false, then that set is inconsistent.

Prove this by our indirect means of "reductio ad absurdum". (That is, you will show an assumption wrong by showing it leads to contradiction.)

Q.E.D.