The Essex-class didn't use F-4 Phantom IIs...they were considered too heavy for their decks. They instead used F-8J Crusaders and A-4E Skyhawks for air to air combat (the A-4E was used on the ASW ships (CVS)) Intrepid was both an attack carrier and a anti-submarine carrier during the Vietnam War.
Apparently one of her A-1H Skyraiders shot down a MIG-17 in 1966.
