This board wouldn’t translate the symbols so I wrote out existential, universal quantifier, and “if, then” instead of the symbol. It should make perfect sense if familiar with formal logic.

existential quantifier x (Fx & ~Gx)
existential quantifier y Fy & universal quantifier x (if Hx then Ixy)
existential quantifier x (Fx & Jx)

Joe, I didn’t bother to transcribe this - which is the only hope I have of taking a hard look at it. It sucks that we can’t use notation here. I have thought about using a bold capital A for a EQ and a bold capital E for a UQ.

I’m not sure where you get the K and the L from in your conclusion. Also, do you mean to say, using my notation, [b]E/band [b]E/band (…)?

Perhaps it would help (me, at least) if you also gave the argumant in plain english. It’s just difficult to know the operations you mean here, given the handicap of not having notational symbols to use.

There exists an x such that both F of x and not G of x
Both There exists a y such that F of y and for every x if H of x then I of x of y
There exists an x such that both F of x and J of x

For every x, there exists a y such that if both K of x and F of y then L of y.

If this is what you mean, then the argument is bad…as Faust pointed out, you have predicates in your conclusion that do not appear in your premises. Additionally, there seems to be some confusion in your use of quantifiers, but it is impossible to tell without knowing what the argument is supposed to be. When I say “argument is bad”, I don’t intend to say that this is an argument in any way, simply that your conclusion cannot follow from you premesis