- #1
hamsterman
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Homework Statement
Prove [itex]\neg x \vee x[/itex] using Hilbert system.
Homework Equations
The logical axioms. I'm not sure if I should state them, or whether there is a standard set. It seems to me that different sets are used. Anyway, the ones with disjunction in them are:
[itex]a \rightarrow a \vee b[/itex]
[itex](a \rightarrow c) \rightarrow ((b \rightarrow c) \rightarrow (a \vee b \rightarrow c))[/itex]
The Attempt at a Solution
If I wanted to use the first axiom, I'd have to prove x, which can be false. If I used the second axiom, I'd get what I wanted on the wrong side of the arrow. I don't think there is a way to reverse an arrow, except for [itex](x \rightarrow y) \rightarrow (\neg y \rightarrow \neg x)[/itex], but then I'd have no way to get rid of the negation. I'm lost. I'd appreciate help.