The universal and ordinary Magisterium is infallible, otherwise almost nothing is:
This is the way infallibility operates most of the time, with extraordinary exercises of the charism—by popes speaking ex cathedra or ecumenical councils giving solemn definitions—being comparatively rare events. When asked about the status of the teaching that the Church has no power to ordain women, the Congregation for the Doctrine of the Faith replied that it is infallible by the infallibility of the ordinary and universal Magisterium.16 Likewise, then-Cardinal Ratzinger and then-Archbishop Bertone, in an article in L’Osservatore Romano, gave as an example of this form of infallibility: “the teaching on the illicitness of prostitution and of fornication.”17
This is relevant to the objection, mentioned in the early paragraphs of this article, that maybe the definition of papal infallibility is wrong because so many of the bishops at Vatican I had left before the vote was taken. A sufficient answer, although not the only one, is that the world’s bishops accepted the definition. Their acceptance is an instance of the infallibility of the ordinary universal Magisterium.
The same applies to decisions of ecumenical councils where a large percentage of the world’s bishops are absent—and that means most of the councils. Councils, including Nicaea, had only a minority of the total bishops when they defined dogmas vital to the very essence of Christianity. Their subsequent acceptance by the world’s episcopate constituted an infallible act of the ordinary universal Magisterium.