Description: Define the subclass relationship. Exercise 9 of TakeutiZaring p. 18.
For example, { 1 , 2 } C_ { 1 , 2 , 3 } ( ex-ss ). Note that
A C_ A (proved in ssid ). Contrast this relationship with the
relationship A C. B (as will be defined in df-pss ). For a more
traditional definition, but requiring a dummy variable, see dfss2 .
Other possible definitions are given by dfss3 , dfss4 , sspss ,
ssequn1 , ssequn2 , sseqin2 , and ssdif0 .

We prefer the label "ss" ("subset") for C_ , despite the fact that it
applies to classes. It is much more common to refer to this as the subset
relation than subclass, especially since most of the time the arguments
are in fact sets (and for pragmatic reasons we don't want to need to use
different operations for sets). The way set.mm is set up, many things are
technically classes despite morally (and provably) being sets, like 1
(cf. df-1 and 1ex ) or RR ( cf. df-r and reex ). This has to
do with the fact that there are no "set expressions": classes are
expressions but there are only set variables in set.mm (cf.
https://us.metamath.org/downloads/grammar-ambiguity.txt ). This is why
we use C_ both for subclass relations and for subset relations and
call it "subset". (Contributed by NM, 27-Apr-1994)