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Hi, I'm flying with Delta From PSA (Italy) to JFK then from JFK to Las Vegas after 4 hours, my flights are:

PISA DL 0137 U 07AUG 1325 UHSX1T 1PC OK
NEW YORK JFK ARRIVAL TIME: 1725
TERMINAL:3

NEW YORK JFK DL 1729 U 07AUG 2129 UHSX1T 1PC OK
TERMINAL:3
LAS VEGAS LAS ARRIVAL TIME: 0012
TERMINAL:1

I'm aware that landing in JFK after the immigration check I have to claim my baggage and check-in again before Las Vegas Flight.
What I need to know is:
do I have to go outside and check-in again just as I'm taking a new flight or there's an internal way to get to another check-in desk dedicated to passengers with connection flights? I'm worried 4 hours aren't really enough !
Thanks
Regards