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Source. Lemma 1, printed p. 144 (PDF p. 2). Put

$$L(c,x)=\exp(c\sqrt{\log x\log\log x}),\qquad \psi(x,y)=\#\{n\le x:p\mid n\Longrightarrow p\le y\}.$$

For every fixed $c>0$, as $x\to\infty$,

$$\psi(x,L(c,x))=x\exp\left(-\left(\frac1{2c}+o(1)\right) \sqrt{\log x\log\log x}\right).$$

Chen imports this analytic estimate from Canfield–Erdős–Pomerance. The exact canonical uniform corollary and its fixed-c interface are already recorded. Their original analytic proof remains external. No uniformity in a varying $c$ is asserted here. Chen only needs $c=1$ in the proof of Lemma 6.