I need to prove that (a → (¬a → b)) is a tautology using only these axioms: 
, Modus Ponens (MP), and Deduction.
Here is the work I have done:
The problem is that it doesn't seem right to suppose "a" is true and then suppose "not a" is true at the same time. I asked my classmates and they did the same in their proofs. Is it really possible to assume two things that contradict each other in deduction? If not, what is the correct way to go about this proof?