Found! It is from Rossini's "Barber of Seville".
There's a funny story attached to this discovery - our dentist has had piano keyboard training, so I thought I'd ask him. His first response was, "My memory sees Bugs Bunny and Elmer Fudd and a barber's chair - doing, I think, the "Barber of Seville"". Thank you, kid's cartoons creators. Many a classical piece has been used in cartoons.
Just in case you'd like a trip down memory lane, here's the YouTube link:
https://www.youtube.com/watch?v=LDLmrEck6kA for Gumble Cartoon - Rabbit of Seville | Looney Tunes | Cartoon World
Ralph Rayner