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Theorem cores 5515
 Description: Restricted first member of a class composition. (Contributed by NM, 12-Oct-2004.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
cores

Proof of Theorem cores
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 vex 3112 . . . . . . 7
2 vex 3112 . . . . . . 7
31, 2brelrn 5238 . . . . . 6
4 ssel 3497 . . . . . 6
5 vex 3112 . . . . . . . 8
65brres 5285 . . . . . . 7
76rbaib 906 . . . . . 6
83, 4, 7syl56 34 . . . . 5
98pm5.32d 639 . . . 4
109exbidv 1714 . . 3
1110opabbidv 4515 . 2
12 df-co 5013 . 2
13 df-co 5013 . 2
1411, 12, 133eqtr4g 2523 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  C_wss 3475   class class class wbr 4452  {copab 4509  rancrn 5005  |`cres 5006  o.ccom 5008 This theorem is referenced by:  cocnvcnv1  5523  cores2  5525  relcoi2  5540  fco2  5747  fcoi2  5765  domss2  7696  canthp1lem2  9052  imasdsval2  14913  frmdss2  16031  gsumval3OLD  16908  gsumval3lem1  16909  gsumzres  16914  gsumzresOLD  16918  gsumzaddlem  16934  gsumzaddlemOLD  16936  dprdf1  17080  kgencn2  20058  tsmsf1o  20647  hhssims  26191  eulerpartgbij  28311  lgamcvg2  28597  cvmlift2lem9a  28748  fourierdlem53  31942  funresfunco  32210 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-xp 5010  df-cnv 5012  df-co 5013  df-dm 5014  df-rn 5015  df-res 5016
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