Proof by reductio ad absurdum

1. Assume there is no necessary thing.

2. Then all things are contingent. (from 1 by definition)

3. "Anything which is capable of not existing at some time or other does not exist." (IP3 168a)

4. "If therefore all things are capable of not existing, [then] there was a time when nothing existed in the Universe." (IP3 168a)

5. "But if this is true, [then] there would also be nothing in existence now . . ." (IP3 168a) ("ex nihil nihil fit")

6. There is something in existence now. (obvious)

7. So, Contradiction: there is nothing in existence but something is in existence.

8. So, there is a necessary thing. (by reductio)