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Theorem rexn0 3932
Description: Restricted existential quantification implies its restriction is nonempty. (Contributed by Szymon Jaroszewicz, 3-Apr-2007.)
Assertion
Ref Expression
rexn0
Distinct variable group:   ,

Proof of Theorem rexn0
StepHypRef Expression
1 ne0i 3790 . . 3
21a1d 25 . 2
32rexlimiv 2943 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  e.wcel 1818  =/=wne 2652  E.wrex 2808   c0 3784
This theorem is referenced by:  reusv2lem3  4655  reusv7OLD  4664  eusvobj2  6289  isdrs2  15568  ismnd  15923  ismndOLD  15926  slwn0  16635  lbsexg  17810  iuncon  19929  grpon0  25204  filbcmb  30231  isbnd2  30279  rencldnfi  30755  stoweidlem14  31796  2reu4  32195  iunconlem2  33735
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-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-ral 2812  df-rex 2813  df-v 3111  df-dif 3478  df-nul 3785
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