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I am working on a predicate logic proof given the following premises:

(For all x)(Fx > Vx)

(There exists x)(Fx & Bx)

Desired conclusion: (There exists) (Vx & Bx)

My instinct here says to use universal elimination on the first premise, generate Vx & Bx as a line, and then use existential introduction to finish it off. Any thoughts on how to approach this? I've done the following so far. Apologies for the poor formatting - I am assuming Fw in line 3.enter image description here

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Using Kevin Klement's natural deduction proof editor and checker here is one solution:

enter image description here

I started with a subproof for existential elimination and then within that subproof used universal elimination. This allowed me to choose the name, "w", in line 3 for existential elimination and use that same name in line 6 for universal elimination.

For more discussion see chapter 32 of P. D. Magnus, Tim Button, J. Robert Loftis, Aaron Thomas-Bolduc, Richard Zach forall x: Calgary Remix.

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