All the bishops participate in the apostolic succession and all the local churches are for this reason in communon with each other. By regarding the Petrine succession and not the apostolic succession of all the bishops as the origin and basis of this power, the pope isolated himself not only from the community of bishop, but also from the whole Church. Seen in this light, it was quite logically consistent for the First Vatican Council to define the decisions made by the pope ex cathedra as irreversable ex sese, non autem ex consensu Ecclesiae.
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About the Archbishop of Australia, see here