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Definition df-pss 2930
Description: Define proper subclass relationship between two classes. Definition 5.9 of [TakeutiZaring] p. 17. Note that ¬ 𝐴𝐴 (proved in pssirr 3041). Contrast this relationship with the relationship 𝐴𝐵 (as defined in df-ss 2928). Other possible definitions are given by dfpss2 3026 and dfpss3 3027. (Contributed by NM, 7-Feb-1996.)
Assertion
Ref Expression
df-pss (𝐴𝐵 ↔ (𝐴𝐵𝐴𝐵))

Detailed syntax breakdown of Definition df-pss
StepHypRef Expression
1 cA . . 3 class 𝐴
2 cB . . 3 class 𝐵
31, 2wpss 2915 . 2 wff 𝐴𝐵
41, 2wss 2914 . . 3 wff 𝐴𝐵
51, 2wne 2204 . . 3 wff 𝐴𝐵
64, 5wa 97 . 2 wff (𝐴𝐵𝐴𝐵)
73, 6wb 98 1 wff (𝐴𝐵 ↔ (𝐴𝐵𝐴𝐵))
Colors of variables: wff set class
This definition is referenced by:  dfpss2  3026  psseq1  3028  psseq2  3029  pssss  3036  pssne  3037  nssinpss  3166  0pss  3262  difsnpssim  3504
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