eolas/zk/Negation_Elimination.md

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---
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tags:
- logic
- propositional-logic
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---
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# Negation Elimination
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Like the [introduction](Negation_Introduction.md) rule for
negation, the elimination rule also works by deriving a contradiction. It is
basically _Negation Introduction_ in reverse. Instead of starting the sub-proof
with a true proposition from which you derive a contradiction, you start with
the negation of a proposition, derive a contradiction and then assert the
positive of the negated proposition you started out with.
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![](/img/negate-elim.png)