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Theorem coss2 4695
 Description: Subclass theorem for composition. (Contributed by NM, 5-Apr-2013.)
Assertion
Ref Expression
coss2

Proof of Theorem coss2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 id 19 . . . . . 6
21ssbrd 3971 . . . . 5
32anim1d 334 . . . 4
43eximdv 1852 . . 3
54ssopab2dv 4200 . 2
6 df-co 4548 . 2
7 df-co 4548 . 2
85, 6, 73sstr4g 3140 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103  wex 1468   wss 3071   class class class wbr 3929  copab 3988   ccom 4543 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-in 3077  df-ss 3084  df-br 3930  df-opab 3990  df-co 4548 This theorem is referenced by:  coeq2  4697  funss  5142  tposss  6143  dftpos4  6160
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