The only use this proof makes of the PA axiom schema of induction is to prove a statement that is axiom (3) above, and so, all computable functions are representable in Q (Mendelson 1997: Th.3.33).
The only use is to prove a statement. This proof makes The only use of the PA axiom schema of induction. This statement is axiom (3) above. All computable functions are representable in Q (Mendelson 1997: Th.3.33). This is so.