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Definition df-ss 3259
 Description: Define the subclass relationship. Exercise 9 of [TakeutiZaring] p. 18. For example, { 1 , 2 } ⊆ { 1 , 2 , 3 } (ex-ss in set.mm). Note that A ⊆ A (proved in ssid 3290). Contrast this relationship with the relationship A ⊊ B (as will be defined in df-pss 3261). For a more traditional definition, but requiring a dummy variable, see dfss2 3262. Other possible definitions are given by dfss3 3263, dfss4 3489, sspss 3368, ssequn1 3433, ssequn2 3436, sseqin2 3474, and ssdif0 3609. (Contributed by NM, 27-Apr-1994.)
Assertion
Ref Expression
df-ss (A B ↔ (AB) = A)

Detailed syntax breakdown of Definition df-ss
StepHypRef Expression
1 cA . . 3 class A
2 cB . . 3 class B
31, 2wss 3257 . 2 wff A B
41, 2cin 3208 . . 3 class (AB)
54, 1wceq 1642 . 2 wff (AB) = A
63, 5wb 176 1 wff (A B ↔ (AB) = A)
 Colors of variables: wff setvar class This definition is referenced by:  dfss  3260  dfss1  3460  inabs  3486  nssinpss  3487  dfrab3ss  3533  disjssun  3608  riinn0  4040  rintn0  4056  dfiota4  4372  ssfin  4470  ssdmres  4987  resabs1  4992
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