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As the Bishop of Rome his assigned church was the Basilica of St. John Lateran.
As pope, his church is St. Peter's Basilica in the Vatican but as Bishop of Rome, his church is the Basilica of St. John Lateran in Rome, Italy.
The pope's church is St. John Lateran. As the bishop of Rome this is his Cathedral. As pope, his church is St. Peter's Basilica.
The First Vatican Council was held in Rome, Italy in the Basilica of St. John Lateran.
The Basilica of St. John Lateran is the official 'home' parish of all popes.