Predicate logic, Every boy who loves a girl is also loved by a girl

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I'm doing some selfstudying and I'm lacking the anwsers to check if I'm correct. So this is why I'm on here so frequently, as I really want to understand the matter.

So here is the sentence I'm trying to convert to predicate logic:

Every boy who loves a girl is also loved by some girl.

DoD = Humans

Here's what I got:

$\forall x(Bx \wedge \exists y(Gy\wedge Lxy))\rightarrow \exists z(Gz \wedge Lzx)$

With B being a boy, G being a Girl, and L x Loving y.

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You are saying here:

If every boy loves a girl then there is a girl that loves some particular boy yet to be specified.

See also my comment.