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content/first-order-logic/axiomatic-deduction/deduction-theorem.tex
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is an axiom, then $\Gamma \Proves !B$. We also have that $\Gamma
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\Proves !B \lif (!A \lif !B)$ by \olref[prp]{ax:lif1}, and
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\olref{prop:mp} gives $\Gamma \Proves !A \lif !B$. If $!B \in \{ !A\}$
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-then $\Gamma \Proves !A \lif !B$ because then last !!{sentence}~$!A
+then $\Gamma \Proves !A \lif !B$ because the last !!{sentence}~$!A
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\lif !B$ is the same as $!A \lif !A$, and we have !!{derive}d that in
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\olref[pro]{ex:identity}.
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