Example of A Proof
Prove: .
Proof:
| Number | Formula | Justification |
|---|---|---|
| 1 | Hypothesis | |
| 2 | Hypothesis | |
| 3 | Universal instantiation | |
| 4 | From (1) and (3) by Modus ponens | |
| 5 | Universal instantiation | |
| 6 | From (2) and (5) by Modus ponens | |
| 7 | From (6) and (4) by Modus ponens | |
| 8 | From (7) by Generalization | |
| 9 | Summary of (1) through (8) | |
| 10 | From (9) by Deduction theorem | |
| 11 | From (10) by Deduction theorem |
In this proof, Universal generalization was used in step 8. The Deduction theorem was applicable in steps 10 and 11 because the formulas being moved have no free variables.
Read more about this topic: Universal Generalization
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