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Theorem abn0 3804
Description: Nonempty class abstraction. (Contributed by NM, 26-Dec-1996.) (Proof shortened by Mario Carneiro, 11-Nov-2016.)
Assertion
Ref Expression
abn0

Proof of Theorem abn0
StepHypRef Expression
1 nfab1 2621 . . 3
21n0f 3793 . 2
3 abid 2444 . . 3
43exbii 1667 . 2
52, 4bitri 249 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  E.wex 1612  e.wcel 1818  {cab 2442  =/=wne 2652   c0 3784
This theorem is referenced by:  rabn0  3805  intexab  4610  iinexg  4612  relimasn  5365  mapprc  7443  modom  7740  tz9.1c  8182  scott0  8325  scott0s  8327  cp  8330  karden  8334  acnrcl  8444  aceq3lem  8522  cff  8649  cff1  8659  cfss  8666  domtriomlem  8843  axdclem  8920  nqpr  9413  supmul  10536  hashf1lem2  12505  hashf1  12506  mreiincl  14993  efgval  16735  efger  16736  birthdaylem3  23283  disjex  27451  disjexc  27452  mppsval  28932  supadd  30042  mblfinlem3  30053  ismblfin  30055  itg2addnc  30069  sdclem1  30236  inisegn0  30989  upbdrech  31505
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-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-nul 3785
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