- #1

millani

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**How do I prove this? (propositional logic)**

## Homework Statement

How to prove this

[itex](p \rightarrow (q \vee p)) \rightarrow r \vdash \neg p \vee (q \vee r)[/itex]

using only the natural deduction rules in propositional logic?

## Homework Equations

http://en.wikipedia.org/wiki/Propositional_logic

(natural deduction rules only)

## The Attempt at a Solution

[itex]1: (p \rightarrow (q \vee p)) \rightarrow r[/itex] premise

<start of hypothesis 0> ; I tried to make a box here but failed miserably

[itex]2: \neg (\neg p \vee (q \vee r))[/itex] hypothesis

<start of hypothesis 1>

[itex]3: \neg p[/itex] hypothesis

[itex]4: \neg p \vee (q \vee r)[/itex] conjunction introduction 3

[itex]5: \bot[/itex] negation introduction 2,4

<end of hypothesis 1>

[itex]6: \neg \neg p[/itex] negation introduction 3-5

[itex]7: p[/itex] double negative elimination 6

[itex]8: ?[/itex]

<end of hypothesis 0>

As you can see, I don't exactly know how to use TeX.

PS: How do I put a box around the hypothesis in TeX?

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