**Description: **Define the relations
class. Proper class relations (like I, cf.
reli 5495) are not elements of it. The element of this
class and the
relation predicate are the same when 𝑅 is a set (cf. elrelsrel 34849).
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 http://us.metamath.org/mpeuni/mathbox.html.
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 (cf.
e.g. df-refs 34872), 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 34847 (cf.
df-refrels 34873 and the resulting dfrefrels2 34875 and dfrefrels3 34876).
3. Finally, in order to be able to work with proper classes (like
iprc 7380) as well, we define the predicate of the
relation (cf.
df-refrel 34874) so that it is true for the relevant proper
classes (cf.
refrelid 34883), and that the element of the class of the
required relations
(e.g. elrefrels3 34880) and this predicate are the same in case of
sets (cf.
elrefrelsrel 34881). (Contributed by Peter Mazsa,
13-Jun-2018.) |