Universal Generalization - Example of A Proof

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.

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