Rules of Inference with Quantifiers

Question

I am having confusion in using the inference rules with quantifiers. For example:

1. ∀x (Man(x) → Mortal(x))
2. Man(Socrates) → Mortal Socrates(x) By Universal Instantiation
3. Man(Socrates) by Premise
4. Mortal(Socrates) By Modus Ponens from step 2 and 3

How do you get the third step? I understand you would need it to use Modus Ponens but how can you write it as a premise and from where did that come from?

Answer 1

It is just a premise. You cannot logically deduce that Socrates is a man - but it is something you assert as part of your proof i.e. a premise. Just like you assert all men are mortals.

1. All men are mortals (Premise)
2. Therefore if Socrates is a man, he is mortal (UI 1)
3. Socrates is a man (Premise)
4. Socrates is mortal (MP 2,3)