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8 lines
348 B
Plaintext
8 lines
348 B
Plaintext
Suppose A -> B. We will show that ~ B -> ~ A.
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It is enough to assume A -> B, ~ B and show ~ A.
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Thus, by rewriting ~ A we may assume A -> B, ~ B and show A -> _|_.
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It is enough to assume A, A -> B, ~ B and show _|_.
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Then, by Modus ponens, we get A, A -> B, B, ~ B to prove _|_.
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In particular we get B, ~ B to prove _|_.
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Hence we get _|_ as desired.
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