The sandwich actually goes farther back than that. When Roman armies were marching to war, it was often to their advantage to move as quickly as possible. How to feed an army on the move? Put the meat on a portable platter....bread! Voila! The sandwich was born.
Of course, it was the Earl of Sandwich that popularized the whole idea and the rest is history.

p.s. A good way to avoid snorting mayonnaise again? Roll up that sandwich inside the lettuce leaves!