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I am doing a proof for my logic class.

The goal is to prove:$$\exists x(P(x)\implies\forall yP(y))$$ from no premises.

I have come to:$$\forall y(P(x)\implies P(x))$$ in my main proof, but I don't know if i have gotten my goal formula in disguise....

What are the rules for moving quantifiers and is my goal sentence implicit in my proven sentence?

drhab
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Adam Nilsson
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  • Welcome to MSE. For some basic information about writing mathematics at this site see, *e.g.*, [basic help on mathjax notation](/help/notation), [mathjax tutorial and quick reference](//math.meta.stackexchange.com/q/5020), [main meta site math tutorial](//meta.stackexchange.com/a/70559) and [equation editing how-to](//math.meta.stackexchange.com/q/1773). – José Carlos Santos Nov 28 '19 at 09:12
  • Thanks for the edit! I am new to the site. – Adam Nilsson Nov 28 '19 at 09:18
  • See also the post [Proof of Drinker Paradox](https://math.stackexchange.com/questions/807092/proof-of-drinker-paradox) – Mauro ALLEGRANZA Nov 28 '19 at 09:40
  • See also [this post](https://math.stackexchange.com/questions/1013720/hilbert-system-with-inference-rule-of-modus-ponens-show-vdash-exists-x-px) – Mauro ALLEGRANZA Nov 28 '19 at 15:26

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