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Theorem eleq1i 2206
 Description: Inference from equality to equivalence of membership. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
eleq1i.1
Assertion
Ref Expression
eleq1i

Proof of Theorem eleq1i
StepHypRef Expression
1 eleq1i.1 . 2
2 eleq1 2203 . 2
31, 2ax-mp 5 1
 Colors of variables: wff set class Syntax hints:   wb 104   wceq 1332   wcel 1481 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-17 1507  ax-ial 1515  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-cleq 2133  df-clel 2136 This theorem is referenced by:  eleq12i  2208  eqeltri  2213  intexrabim  4086  abssexg  4114  abnex  4376  snnex  4377  pwexb  4403  sucexb  4421  omex  4515  iprc  4815  dfse2  4920  fressnfv  5615  fnotovb  5822  f1stres  6065  f2ndres  6066  ottposg  6160  dftpos4  6168  frecabex  6303  oacl  6364  diffifi  6796  djuexb  6937  pitonn  7681  axicn  7696  pnfnre  7832  mnfnre  7833  0mnnnnn0  9034  nprmi  11842  txdis1cn  12487  xmeterval  12644  expcncf  12801  bj-sucexg  13292
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