Complex sentence: 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).
Split into simpler sentences: The only use this proof makes of the PA axiom schema of induction is to prove a statement that is axiom (3) above. Moreover, all computable functions are representable in Q (Mendelson 1997: Th.3.33).