On page 112 of Bollobás' book Modern Graph Theory, Lemma 9's conclusion includes the following inequality:
I understand the proof of this lemma up to the following inequality:
But then the last sentence of the proof seems to imply that the left side of inequality (3) is at least the left side of inequality (2). This implication may follow from some use of convexity but I don't see it. How is this implication proved?