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Theorem coss1 4434
Description: Subclass theorem for composition. (Contributed by FL, 30-Dec-2010.)
Assertion
Ref Expression
coss1 
C_  o.  C  C_  o.  C

Proof of Theorem coss1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 id 19 . . . . . 6 
C_  C_
21ssbrd 3796 . . . . 5 
C_
32anim2d 320 . . . 4 
C_  C  C
43eximdv 1757 . . 3 
C_  C  C
54ssopab2dv 4006 . 2 
C_  { <. ,  >.  |  C  }  C_  {
<. ,  >.  |  C  }
6 df-co 4297 . 2  o.  C  { <. , 
>.  |  C  }
7 df-co 4297 . 2  o.  C  { <. , 
>.  |  C  }
85, 6, 73sstr4g 2980 1 
C_  o.  C  C_  o.  C
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  wex 1378    C_ wss 2911   class class class wbr 3755   {copab 3808    o. ccom 4292
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-bndl 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-in 2918  df-ss 2925  df-br 3756  df-opab 3810  df-co 4297
This theorem is referenced by:  coeq1  4436  funss  4863  tposss  5802
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