Description: Define the relations
class. Proper class relations (like I, see
reli 5822) are not elements of it. The element of this
class and the
relation predicate are the same when 𝑅 is a set (see elrelsrel 37953).
The class of relations is a great tool we can use when we define classes
of different relations as nullary class constants as required by the 2.
point in our Guidelines https://us.metamath.org/mpeuni/mathbox.html 37953.
When we want to define a specific class of relations as a nullary class
constant, the appropriate method is the following:
1. We define the specific nullary class constant for general sets (see
e.g. df-refs 37976), then
2. we get the required class of relations by the intersection of the class
of general sets above with the class of relations df-rels 37951 (see
df-refrels 37977 and the resulting dfrefrels2 37979 and dfrefrels3 37980).
3. Finally, in order to be able to work with proper classes (like
iprc 7913) as well, we define the predicate of the
relation (see
df-refrel 37978) so that it is true for the relevant proper
classes (see
refrelid 37988), and that the element of the class of the
required relations
(e.g. elrefrels3 37985) and this predicate are the same in case of
sets (see
elrefrelsrel 37986). (Contributed by Peter Mazsa,
13-Jun-2018.) |