Quantifier change: from exist to forall?

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For instance, I want to prove ;

$\exists xp(x) \vdash \forall y p(y)$

is valid.

Can the proof itself be valid? And what the idea behind this proof stands for?

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This is definitely not valid. Think about it: you are basically saying "Since something has property P, everything has property P". For example, "Since 2 is an even number, everything is an even number"??!?