Suppose we wish to show
{ } |- (a1 AND (a2 AND ... a100)) -> a1 
using the rules we discussed in class today.

One way of doing this would be as follows:

1. { a1 AND (a2 AND ... a100)) } |-  a1 AND (a2 AND ... a100)
           -- by Assumption rule

2. { a1 AND (a2 AND ... a100)) } |- a1
           -- by 1 above and AND-elimination rule

3. { } |-  (a1 AND (a2 AND ... a100)) -> a1
           -- by 2 above and IMPLICATION-introduction rule