Definition df-pss 3261

Description: Define proper subclass relationship between two classes. Definition 5.9 of [TakeutiZaring] p. 17. For example, { 1 , 2 } C. { 1 , 2 , 3 } (ex-pss in set.mm). Note that -. A C. A (proved in pssirr 3369). Contrast this relationship with the relationship A C_ B (as defined in df-ss 3259). Other possible definitions are given by dfpss2 3354 and dfpss3 3355. (Contributed by NM, 7-Feb-1996.)

Assertion

Ref	Expression
df-pss	|- (A C. B <-> (A C_ B /\ A =/= B))

Detailed syntax breakdown of Definition df-pss

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cB	. . 3 class B
3	1, 2	wpss 3258	. 2 wff A C. B
4	1, 2	wss 3257	. . 3 wff A C_ B
5	1, 2	wne 2516	. . 3 wff A =/= B
6	4, 5	wa 358	. 2 wff (A C_ B /\ A =/= B)
7	3, 6	wb 176	1 wff (A C. B <-> (A C_ B /\ A =/= B))

This definition is referenced by:  dfpss2  3354  psseq1  3356  psseq2  3357  pssss  3364  pssne  3365  nssinpss  3487  0pss  3588  pssdif  3612  difsnpss  3851  sfinltfin  4535