I asked my bird vet about the same thing and that is what he told me. But he also said to keep the egg to a lower amount each day, like one piece the size of the bird's beak is enough egg for one day.
Hope this helps.
EDIT: About the bread... It is usually safe.
James Harris, DVM is owner and medical director of the Mayfair Veterinary Clinic in Sandy Bay says, "While eating bread can raise the level of yeast found in droppings, the yeast that is used in baking bread does NOT cause disease."
Bread is dangerous for parrots and birds in general. They can get yeast infections in their crop. Also your parrot doesn't have enough leafy greens - those are what should compose MOST of their daily diets.
I live in a country where there are no bird pellets but mixture of seeds(sunflower, millet, etc). So I feed my bird a mixture of seeds, fruits(apples, guavava, peach, banana, orange etc) and vegetables(carrot, sweetpepper, corn, bread,egg etc). Is this diet okay. Can my parrot do without the pellets and remain healthy if i continue with the fresh fruits and veggies. Will it be okay without pellets.