It was inferred. After all they were symbolic keys and the point was they were all given these powers. Instead of looking for keys you should have been looking for evidence they were given these powers. The gates with their names on them should have sufficed in that regard.
Peace be with you
It was inferred.
I believe you meant “It was implied.” Either that, or you meant to write “It is what I inferred.”
The keys and bindings were for The Church Age, and Peter was given the honor of this 'opening the mystery' of the Ekklesia because of his profession revealed to him by the Holy Spirit. The 'opening act' is seen in Acts 2, the Day of Pentecost, fifty days after the Passover. [See Romans 16: 25&26, and Ephesians 3:3-7]
Jesus did not appoint Peter to be the 'papa' of the Ekkelsia. Jesus gave Peter the honor of opening the doorway for the Ekklesia who are Saved by Faith in Jesus The Christ.