I will use the same table as in ponderable 1.1.1. Now, there are three variables, each can be T or F, so the table needs 23=8 rows. We must verify that the third ⇒ column is filled with T.
| ((p | ⇒ | q) | ∧ | (q | ⇒ | r)) | ⇒ | (p | ⇒ | r) |
|---|---|---|---|---|---|---|---|---|---|---|
| T | T | T | T | T | T | T | T | T | T | T |
| T | T | T | F | T | F | F | T | T | F | F |
| T | F | F | F | F | T | T | T | T | T | T |
| T | F | F | F | F | T | F | T | T | F | F |
| F | T | T | T | T | T | T | T | F | T | T |
| F | T | T | F | T | F | F | T | F | T | F |
| F | T | F | T | F | T | T | T | F | T | T |
| F | T | F | T | F | T | F | T | F | T | F |
QED.