What is the proof that electron degeneracy pressure exists in earth and other planets (including asteroids)?
If electron degeneracy pressure didn't exist in planets they would collapse into neutronium.
An atom consists of a small nucleus surrounded by electron shells. Electron degeneracy pressure prevents the electron shells of two atoms from overlapping. This is due to the Pauli exclusion principle which prevents more than one electron being in the same quantum state.
This is the reason why you don't fall through the floor. Any solid object has its atoms kept apart by electron degeneracy pressure.
The only objects where electron degeneracy pressure doesn't exist are neutron stars and black holes. If electron degeneracy pressure is overcome by gravity the object collapses and the electrons are expelled and the nuclei merge. The protons get converted into neutrons.
This collapse can only happen in very massive objects. The only know objects which can overcome electron degeneracy pressure due to collapse are the cores of large stars which have run out of nuclear fuel.
So, we can be certain that all objects other than neutron stars and black holes have electron degeneracy pressure. Planets and other objects are not massive enough for gravity to overcome it.