  In this paper $\mathrm{NFU}^{-\mathrm{AC}}$ is used to denote Ronald Jensen's
modification of Quine's `New Foundations' Set Theory ($\mathrm{NF}$) fortified
with a type-level pairing function but without the Axiom of Choice. The axiom
$\mathrm{AxCount}_\geq$ is the variant of the Axiom of Counting which asserts
that no finite set is smaller than its own set of singletons. This paper shows
that $\mathrm{NFU}^{-\mathrm{AC}}+\mathrm{AxCount}_\geq$ proves the consistency
of the Simple Theory of Types with Infinity ($\mathrm{TSTI}$). This result
implies that $\mathrm{NF}+\mathrm{AxCount}_\geq$ proves that consistency of
$\mathrm{TSTI}$, and that $\mathrm{NFU}^{-\mathrm{AC}}+\mathrm{AxCount}_\geq$
proves the consistency of $\mathrm{NFU}^{-\mathrm{AC}}$.
