An inequality related to the sieve of Eratosthenes

Let $\mathrm{\Phi }(x,y)$ denote the number of integers $n\in [1,x]$ free of prime factors $\le y$. We show that but for a few small cases, $\mathrm{\Phi }(x,y)<.6x\mathrm{/}\log y$ when $y\le \sqrt{x}$.