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Definition df-pss 2911
Description: Define proper subclass relationship between two classes. Definition 5.9 of [TakeutiZaring] p. 17. Note that ¬ AA (proved in pssirr 3022). Contrast this relationship with the relationship AB (as defined in df-ss 2909). Other possible definitions are given by dfpss2 3007 and dfpss3 3008. (Contributed by NM, 7-Feb-1996.)
Assertion
Ref Expression
df-pss (AB ↔ (AB AB))

Detailed syntax breakdown of Definition df-pss
StepHypRef Expression
1 cA . . 3 class A
2 cB . . 3 class B
31, 2wpss 2896 . 2 wff AB
41, 2wss 2895 . . 3 wff AB
51, 2wne 2186 . . 3 wff AB
64, 5wa 97 . 2 wff (AB AB)
73, 6wb 98 1 wff (AB ↔ (AB AB))
Colors of variables: wff set class
This definition is referenced by:  dfpss2  3007  psseq1  3009  psseq2  3010  pssss  3017  pssne  3018  nssinpss  3147  0pss  3243  difsnpssim  3458
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