Equivalent formulas

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I'm not exactly sure how to lay this out, but this is based on page 32 in

Statement/Definition

There's something in the second to last paragraph of page 32 in

Examples

Recall [ilmath]\models A[/ilmath] denotes that a formula is valid.

1. [ilmath]\models(A\wedge B)\leftrightarrow\neg(\neg A\vee \neg B)[/ilmath]
2. [ilmath]\models(A\rightarrow B)\leftrightarrow\neg A\vee B[/ilmath] (see negation of implies)
3. [ilmath]\models(A\leftrightarrow B)\leftrightarrow\neg(\neg(\neg A\vee B)\vee\neg(\neg B\vee A))[/ilmath], not even sure I've written this down correctly, never used it
4. [ilmath]\models(\forall x A)\leftrightarrow\neg(\exists x\neg A)[/ilmath] (would be good one to prove!)

Proofs

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See page 32 in