Question

Given: p is true

Answer 1

I put D and it was correct.

Answer 2

The answer:
according the statement  
"Assume p and ~q are both true. ~q → r, and r → ~p. Therefore, ~p and p cannot be true, so p and ~q cannot be true. Therefore, p → q is true."
the answerer has just used theorem between combination of ¬p, p, ¬q and q. 

that is called theorem of mathematics logic,

so the proof is  D. proof by theorem