What do the dogs refer to as Animalism?

In Orwell's book, the dogs and pigs form an exclusive group after Snowball's ouster. The new pig leader, Napoleon, is never seen without his army of nine ferocious dogs.
We must remember that Animalism originally consisted of seven rules. Here they are:

Whatever goes upon two legs is an enemy.
Whatever goes upon four legs, or has wings, is a friend.
No animal shall wear clothes.
No animal shall sleep in a bed.
No animal shall drink alcohol.
No animal shall kill any other animal.
All animals are equal.

Basically, Animalism demands that animals distinguish themselves from humans. It also demands that animals refuse to accept the supremacy of humans. Indeed, the central tenet of Animalism rests on the right of all animals to be free from enslavement (to humans). However, the rules of Animalism soon change after Snowball's ouster from the farm.
The pigs and dogs slowly take on the habits of their previous human masters. They sleep on beds, drink alcohol, and wear human clothing. While rations for the other animals are reduced, the pigs and dogs excuse themselves from such a sacrifice. Thus, the new Animalism (according to the dogs and the pigs) rests on just one rule: all animals are equal but some animals are more equal than others. Like the pigs, the dogs believe that they have every right to the privileged positions once occupied by their human masters.