YES! Italians use oil (Olive) and vinegar seperately.They don't mix egg into oil without useing some spice,as Tyme,Basil etc.Mayo is French and some Italian sandwiches,mostly cold cuts with out lettuce use Mayo.But subs ...NO. The sub originated in Italian Deli's in USA and was a way to use up the oddly cut and end cuts of lunch meat.They were put on a "sub" shaped bun.The "Poor boy " was the same sandwich but was served on slices of bread,preferable an artisan bread.
Lettuce was added later as refrigeration came into play but the original lettuce was actually cabbage because it didn't require refrigeration.I still prefer my subs and poorboys with thinly shreded cabbage and vinegar and oil, but mayo is good with corned beef and rye.
Mind you things change but I'm talking about the originals.
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I'm so old I remember this stuff!