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Theorem coeq2 4697
 Description: Equality theorem for composition of two classes. (Contributed by NM, 3-Jan-1997.)
Assertion
Ref Expression
coeq2

Proof of Theorem coeq2
StepHypRef Expression
1 coss2 4695 . . 3
2 coss2 4695 . . 3
31, 2anim12i 336 . 2
4 eqss 3112 . 2
5 eqss 3112 . 2
63, 4, 53imtr4i 200 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1331   wss 3071   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:  coeq2i  4699  coeq2d  4701  coi2  5055  relcnvtr  5058  relcoi1  5070  f1eqcocnv  5692  ereq1  6436  upxp  12441  uptx  12443  txcn  12444
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