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Definition df-pss 2051
Description: Define proper subclass relationship between two classes. Definition 5.9 of [TakeutiZaring] p. 17. Other possible definitions are given by dfpss2 2129 and dfpss3 2130.
Assertion
Ref Expression
df-pss |- (A (. B <-> (A (_ B /\ A =/= B))
Detailed syntax breakdown of Definition df-pss
StepHypRef Expression
1 cA . . 3 class A
2 cB . . 3 class B
31, 2wpss 2044 . 2 wff A (. B
41, 2wss 2043 . . 3 wff A (_ B
51, 2wne 1582 . . 3 wff A =/= B
64, 5wa 223 . 2 wff (A (_ B /\ A =/= B)
73, 6wb 146 1 wff (A (. B <-> (A (_ B /\ A =/= B))
Colors of variables: wff set class
This definition is referenced by:  dfpss2 2129  psseq1 2131  psseq2 2132  pssss 2139  0pss 2304  pssnel 2327  ordelpss 2970  ominf 4514  inf3lem2 4594  inf3lem4 4596  infeq5 4601  ch0psst 9307
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