Is it correct to put bound variables inside logical functions?

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I have to translate this sentence to predicate logic:

Every animal either likes to eat all plants or all animals much smaller than itself that like to eat some plants.

Clearly I have to distinguish animals that like to eat some- and all plants. I define the function eats(x,y)=x likes to eat y.

So is it correct to write something like eats(x, all(y)[whatever(y)])?Can a bound variable be inside a function like this?