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Theorem coss2 4438
Description: Subclass theorem for composition. (Contributed by NM, 5-Apr-2013.)
Assertion
Ref Expression
coss2 
C_  C  o.  C_  C  o.

Proof of Theorem coss2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 id 19 . . . . . 6 
C_  C_
21ssbrd 3799 . . . . 5 
C_
32anim1d 319 . . . 4 
C_  C  C
43eximdv 1760 . . 3 
C_  C  C
54ssopab2dv 4009 . 2 
C_  { <. ,  >.  |  C }  C_  {
<. ,  >.  |  C }
6 df-co 4300 . 2  C  o.  { <. , 
>.  |  C }
7 df-co 4300 . 2  C  o.  { <. , 
>.  |  C }
85, 6, 73sstr4g 2983 1 
C_  C  o.  C_  C  o.
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97  wex 1381    C_ wss 2914   class class class wbr 3758   {copab 3811    o. ccom 4295
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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-in 2921  df-ss 2928  df-br 3759  df-opab 3813  df-co 4300
This theorem is referenced by:  coeq2  4440  funss  4866  tposss  5806  dftpos4  5823
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