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Theorem elrn 5248
Description: Membership in a range. (Contributed by NM, 2-Apr-2004.)
Hypothesis
Ref Expression
elrn.1
Assertion
Ref Expression
elrn
Distinct variable groups:   ,   ,

Proof of Theorem elrn
StepHypRef Expression
1 elrn.1 . . 3
21elrn2 5247 . 2
3 df-br 4453 . . 3
43exbii 1667 . 2
52, 4bitr4i 252 1
Colors of variables: wff setvar class
Syntax hints:  <->wb 184  E.wex 1612  e.wcel 1818   cvv 3109  <.cop 4035   class class class wbr 4452  rancrn 5005
This theorem is referenced by:  dmcosseq  5269  rnco  5518  dffo4  6047  fvclss  6154  rntpos  6987  fpwwe2lem11  9039  fpwwe2lem12  9040  fclim  13376  perfdvf  22307  dftr6  29179  dffr5  29182  brsset  29539  dfon3  29542  brtxpsd  29544  dffix2  29555  elsingles  29568  dfrdg4  29600  inisegn0  30989
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-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-cnv 5012  df-dm 5014  df-rn 5015
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