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What did propeller aircraft use to shoot down a MiG three days after the Phantom's first combat?
Short answer
With their cannons. On June 20, 1965, two A-1H Skyraiders from VA-25 "Fist of the Fleet," embarked on USS Midway (CVA-41), were attacked by MiG-17s while supporting the rescue of a USAF pilot in northwestern North Vietnam and shot one down with their four 20 mm M3 cannons.

A rescue in northwestern North Vietnam
On June 20, 1965, a formation of Skyraiders from Strike Squadron 25 (VA-25), nicknamed "Fist of the Fleet," took off from USS Midway (CVA-41) to support the rescue of a USAF pilot shot down in the far northwest of North Vietnam. During the mission they were attacked by a formation of MiG-17s. At the controls of the two A-1Hs that carried out the shootdown were Lieutenant Charles W. Hartman III, in BuNo 137523, call sign "Canasta 573," and Lieutenant Clinton B. Johnson, in BuNo 139768, "Canasta 577."
Four 20 mm M3 cannons
The A-1H carried four fixed, forward-firing 20 mm M3 cannons, capable of firing 800 rounds per minute. The Skyraiders maneuvered to line up one of the MiGs and shot it down with that armament.
Johnson's account is terse: both fired with all four cannons; Hartman's hits appeared to enter through the intake and wing root, and his own rounds raked the top of the fuselage and went through the cockpit. The fighter did not return fire: it banked, rolled inverted and crashed into a small hill, where it exploded and burned in a cultivated field.
The last piston engine against a jet
The Skyraider was the last piston-engine aircraft to shoot down a jet fighter, and that June 20 was not its only victory. On October 9, 1966, four A-1Hs from VA-176, embarked on USS Intrepid, were attacked by four MiG-17s during a rescue support patrol; Lieutenant William T. Patton, call sign "Papoose 409," shot down one of them.
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