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12 lines
780 B
12 lines
780 B
\begin{equation*}
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\begin{split}
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x \leftrightarrow (p \rightarrow q) &\Leftrightarrow x \leftrightarrow (p \rightarrow q)\\
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&\Leftrightarrow (x \rightarrow (p \rightarrow q)) \land ((p \rightarrow q) \rightarrow x)\\
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&\Leftrightarrow (x \rightarrow (\lnot p \lor q)) \land ((\lnot p \lor q) \rightarrow x)\\
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&\Leftrightarrow (\lnot x \lor (\lnot p \lor q)) \land (\lnot (\lnot p \lor q) \lor x)\\
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&\Leftrightarrow (\lnot x \lor \lnot p \lor q) \land ((\lnot\lnot p \land \lnot q) \lor x)\\
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&\Leftrightarrow (\lnot x \lor \lnot p \lor q) \land ((p \land \lnot q) \lor x)\\
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&\Leftrightarrow (\lnot x \lor \lnot p \lor q) \land ((p \lor x) \land (\lnot q \lor x))\\
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&\Leftrightarrow (\lnot x \lor \lnot p \lor q) \land (p \lor x) \land (\lnot q \lor x)\\
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\end{split}
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\end{equation*}
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