Formal Proof in Propositional Logic - Explanation?

Question

Could somebody explain what is happening here? I understood formal proof until the example questions I was reviewing started to include a tick symbol in the answers. The exercise is to write a formal proof for the following:

(p ∧ q) ⇒ r ⊢ p ⇒ (q ⇒ r )

This is the answer provided

I understand the assumptions made and the use of rules of inference but what is happening when a tick is used?

Answer 1

Your answer key seems to be writing down the desired statement to be proven before proceeding to prove it, and after that marking it with a tick when done. For example in the case of the second tick the line 2.2 is proven from lines 2.2.1 to 2.2.3. Of course, mathematically it is irrelevant to the formal proof, but in practice it is useful to be able to distinguish between what you aim to prove and what you have succeeded in proving.