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Theorem elima3 5019
 Description: Membership in an image. Theorem 34 of [Suppes] p. 65. (Contributed by NM, 14-Aug-1994.)
Hypothesis
Ref Expression
elima.1
Assertion
Ref Expression
elima3
Distinct variable groups:   ,   ,   ,

Proof of Theorem elima3
StepHypRef Expression
1 elima.1 . . 3
21elima2 5018 . 2
3 df-br 4024 . . . 4
43anbi2i 675 . . 3
54exbii 1569 . 2
62, 5bitri 240 1
 Colors of variables: wff set class Syntax hints:   wb 176   wa 358  wex 1528   wcel 1684  cvv 2788  cop 3643   class class class wbr 4023  cima 4692 This theorem is referenced by:  cnvresima  5162  imaiun  5771  cnvresimaOLD  26226 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-br 4024  df-opab 4078  df-xp 4695  df-cnv 4697  df-dm 4699  df-rn 4700  df-res 4701  df-ima 4702
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