Definition df-pss 2055

Description: Define proper subclass relationship between two classes. Definition 5.9 of [TakeutiZaring] p. 17. Other possible definitions are given by dfpss2 2133 and dfpss3 2134.

Assertion

Ref	Expression
df-pss	|- (A (. B <-> (A (_ 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 2048	. 2 wff A (. B
4	1, 2	wss 2047	. . 3 wff A (_ B
5	1, 2	wne 1585	. . 3 wff A =/= B
6	4, 5	wa 223	. 2 wff (A (_ B /\ A =/= B)
7	3, 6	wb 146	1 wff (A (. B <-> (A (_ B /\ A =/= B))

This definition is referenced by:  dfpss2 2133  psseq1 2135  psseq2 2136  pssss 2143  0pss 2308  pssnel 2331  ordelpss 2975  ominfOLD 4529  inf3lem2 4614  inf3lem4 4616  infeq5 4621  ch0psst 9369  sfseqeq 10543  top2usne 10549

Copyright terms: Public domain