Since the event fires once, and mousemovefires every time you move it by a pixel, you can simply ignore the very first (possibly automatic, depending on the browser) event mousemoveto get the desired effect, for example
$(function() {
var moveCount = 0;
$("html").mousemove(function () {
if(moveCount++ === 0) return;
$("p").fadeOut("slow");
$(this).unbind('mousemove');
});
});
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