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Definition df-pss 3261
Description: Define proper subclass relationship between two classes. Definition 5.9 of [TakeutiZaring] p. 17. For example, { 1 , 2 } ⊊ { 1 , 2 , 3 } (ex-pss in set.mm). Note that ¬ AA (proved in pssirr 3369). Contrast this relationship with the relationship A 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 (AB ↔ (A B AB))

Detailed syntax breakdown of Definition df-pss
StepHypRef Expression
1 cA . . 3 class A
2 cB . . 3 class B
31, 2wpss 3258 . 2 wff AB
41, 2wss 3257 . . 3 wff A B
51, 2wne 2516 . . 3 wff AB
64, 5wa 358 . 2 wff (A B AB)
73, 6wb 176 1 wff (AB ↔ (A B AB))
Colors of variables: wff setvar class
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
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