Use equational proof to solve the problem.
$ \vdash A \lor (B \rightarrow A) \equiv B \rightarrow A $
These are the axioms and theorems.
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Use: $B\rightarrow A\equiv\lnot B\lor A$ – b00n heT Feb 04 '14 at 07:22
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Did you just want to share this with us or is there a question somewhere in here? – 5xum Feb 04 '14 at 07:23
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Prove this $ \vdash A \lor (B \rightarrow A) \equiv B \rightarrow A $ That's the question. – Out Of Bounds Feb 04 '14 at 07:24
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@b00nheT I used it but could't continue. – Out Of Bounds Feb 04 '14 at 07:25
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$ A \lor (B \rightarrow A) = A \lor (\lnot B\lor A)= (\lnot B\lor A)\lor A= \lnot B\lor (A\lor A)=\lnot B\lor A = B \rightarrow A$ – Jose Antonio Feb 04 '14 at 07:27
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@JoseAntonio Can you help me with this one ? $ A \lor A \lor A \vdash B \rightarrow A $ – Out Of Bounds Feb 04 '14 at 08:39