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## Homework Statement

Using the rules of inference, prove that if ∀x(P(x) ∨ Q(x)) and ∀x((￢P(x) ∧ Q(x)) → R(x)) are true, then ∀x(￢R(x) → P(x)) is true as well.

## Homework Equations

## The Attempt at a Solution

The problem arises step 5. I feel this is correct but the instructor has stated that assuming in a proof:

"you are not allowed to assume any more information that what is given. Otherwise, you are solving a different problem."

I felt since my assumption is a bit like a scenario in a truth table that it was OK, because it does not contradict any of the premises.

I have no idea how to approach this problem other than this.