Definition df-pss 2933

Description: Define proper subclass relationship between two classes. Definition 5.9 of [TakeutiZaring] p. 17. Note that -. A C. A (proved in pssirr 3044). Contrast this relationship with the relationship A C_ B (as defined in df-ss 2931). Other possible definitions are given by dfpss2 3029 and dfpss3 3030. (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 2918	. 2 wff A C. B
4	1, 2	wss 2917	. . 3 wff A C_ B
5	1, 2	wne 2204	. . 3 wff A =/= B
6	4, 5	wa 97	. 2 wff ( A C_ B /\ A =/= B )
7	3, 6	wb 98	1 wff ( A C. B <-> ( A C_ B /\ A =/= B ) )

This definition is referenced by:  dfpss2  3029  psseq1  3031  psseq2  3032  pssss  3039  pssne  3040  nssinpss  3169  0pss  3265  difsnpssim  3507