# Category:Proof by Contradiction

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This category contains pages concerning **Proof by Contradiction**:

**Proof by contradiction** is a valid argument in types of logic dealing with negation $\neg$ and contradiction $\bot$.

This includes classical propositional logic and predicate logic, and in particular natural deduction.

### Proof Rule

- If, by making an assumption $\phi$, we can infer a contradiction as a consequence, then we may infer $\neg \phi$.

- The conclusion $\neg \phi$ does not depend upon the assumption $\phi$.

## Pages in category "Proof by Contradiction"

The following 15 pages are in this category, out of 15 total.

### P

- Proof by Contradiction
- Proof by Contradiction for Hilbert Proof System Instance 1 for Predicate Logic
- Proof by Contradiction/Also known as
- Proof by Contradiction/Explanation
- Proof by Contradiction/Proof Rule
- Proof by Contradiction/Sequent Form
- Proof by Contradiction/Variant 1
- Proof by Contradiction/Variant 2
- Proof by Contradiction/Variant 2/Formulation 1
- Proof by Contradiction/Variant 2/Formulation 2
- Proof by Contradiction/Variant 3
- Proof by Contradiction/Variant 3/Formulation 1
- Proof by Contradiction/Variant 3/Formulation 2
- Proof by Contradiction/Variant 3/Formulation 2/Proof 1
- Proof by Contradiction/Variant 3/Formulation 2/Proof 2