Something is a “property” means that you can use that “property” to separate objects into two groups, such that all the members of one group have that “property”, while all the members of another group have not.
For example, “being big” is a property of some dogs, because you can separate all the dogs into two groups: group with big dogs and group with non-big dogs.
However, “existence” is not a property of any dogs, because you cannot separate all the dogs into two groups, such that one has existing dogs and one has non-existing dogs.
The existence of a dog is not a property of the dog itself. Instead, the existence of a dog is a property of, for example, rooms.
You can use “the existence of dogs” to separate all the rooms in this world into two groups: the room with dogs and the room without dogs.
— Me@2012-10-18 12:47:32 PM
— Me@2014-03-03 02:46:35 PM
2014.03.03 Monday (c) All rights reserved by ACHK