From the Gospel of Matthew; (Matt: 16:17-19)
17 Jesus said to him in reply, "Blessed are you, Simon son of Jonah. For flesh and blood 12 has not revealed this to you, but my heavenly Father. 18 And so I say to you, you are Peter, and upon this rock I will build my church, 13 and the gates of the netherworld shall not prevail against it. 19 I will give you the keys to the kingdom of heaven. 14 Whatever you bind on earth shall be bound in heaven; and whatever you loose on earth shall be loosed in heaven."
and again; (Matt 28: 18-20)
18 Then Jesus approached and said to them, "All power in heaven and on earth has been given to me. 19 Go, therefore, and make disciples of all nations, baptizing them in the name of the Father, and of the Son, and of the holy Spirit, 20 teaching them to observe all that I have commanded you. And behold, I am with you always, until the end of the age."
I don't know about anybody else but the Catholic church is't going anywhere until the end of time.