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Theorem ssrab 3012
Description: Subclass of a restricted class abstraction. (Contributed by NM, 16-Aug-2006.)
Assertion
Ref Expression
ssrab 
C_  {  |  }  C_
Distinct variable groups:   ,   ,
Allowed substitution hint:   ()

Proof of Theorem ssrab
StepHypRef Expression
1 df-rab 2309 . . 3  {  |  }  {  |  }
21sseq2i 2964 . 2 
C_  {  |  }  C_  {  |  }
3 ssab 3004 . 2 
C_  {  |  }
4 dfss3 2929 . . . 4 
C_
54anbi1i 431 . . 3  C_
6 r19.26 2435 . . 3
7 df-ral 2305 . . 3
85, 6, 73bitr2ri 198 . 2 
C_
92, 3, 83bitri 195 1 
C_  {  |  }  C_
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240   wcel 1390   {cab 2023  wral 2300   {crab 2304    C_ wss 2911
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rab 2309  df-in 2918  df-ss 2925
This theorem is referenced by:  ssrabdv  3013
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