Going through a book on formal logic, I have encountered the following problem. Since I am somewhat new to formal logic, I am confused about how to approach it.
A certain formal theory has exactly two axioms:
(a) 2 + 2 = 4 -> (2 + 2 = 4 -> 2 + 3 = 6) (b) 2 + 2 = 4
and has modus ponens, i.e.,
(P->Q, P) -> Q
Find all theorems of this theory.
I understand that the axioms themselves are theorems. How can I find the others?