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Theorem limeq 4895
 Description: Equality theorem for the limit predicate. (Contributed by NM, 22-Apr-1994.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
limeq

Proof of Theorem limeq
StepHypRef Expression
1 ordeq 4890 . . 3
2 neeq1 2738 . . 3
3 id 22 . . . 4
4 unieq 4257 . . . 4
53, 4eqeq12d 2479 . . 3
61, 2, 53anbi123d 1299 . 2
7 df-lim 4888 . 2
8 df-lim 4888 . 2
96, 7, 83bitr4g 288 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\w3a 973  =wceq 1395  =/=wne 2652   c0 3784  U.cuni 4249  Ordword 4882  Limwlim 4884 This theorem is referenced by:  limuni2  4944  0ellim  4945  limuni3  6687  tfinds2  6698  dfom2  6702  limomss  6705  nnlim  6713  limom  6715  ssnlim  6718  onfununi  7031  tfr1a  7082  tz7.44lem1  7090  tz7.44-2  7092  tz7.44-3  7093  oeeulem  7269  limensuc  7714  elom3  8086  r1funlim  8205  rankxplim2  8319  rankxplim3  8320  rankxpsuc  8321  infxpenlem  8412  alephislim  8485  cflim2  8664  winalim  9094  rankcf  9176  gruina  9217  rdgprc0  29226  dfrdg2  29228  dfrdg4  29600  limsucncmpi  29910  limsucncmp  29911 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-3an 975  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-in 3482  df-ss 3489  df-uni 4250  df-tr 4546  df-po 4805  df-so 4806  df-fr 4843  df-we 4845  df-ord 4886  df-lim 4888
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