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Theorem inex1 3861
Description: Separation Scheme (Aussonderung) using class notation. Compare Exercise 4 of [TakeutiZaring] p. 22. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
inex1.1  _V
Assertion
Ref Expression
inex1  i^i 
_V

Proof of Theorem inex1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 inex1.1 . . . 4  _V
21zfauscl 3847 . . 3
3 dfcleq 2012 . . . . 5  i^i  i^i
4 elin 3099 . . . . . . 7  i^i
54bibi2i 216 . . . . . 6  i^i
65albii 1335 . . . . 5  i^i
73, 6bitri 173 . . . 4  i^i
87exbii 1474 . . 3  i^i
92, 8mpbir 134 . 2  i^i
109issetri 2538 1  i^i 
_V
Colors of variables: wff set class
Syntax hints:   wa 97   wb 98  wal 1224   wceq 1226  wex 1358   wcel 1370   _Vcvv 2531    i^i cin 2889
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 617  ax-5 1312  ax-7 1313  ax-gen 1314  ax-ie1 1359  ax-ie2 1360  ax-8 1372  ax-10 1373  ax-11 1374  ax-i12 1375  ax-bnd 1376  ax-4 1377  ax-17 1396  ax-i9 1400  ax-ial 1405  ax-i5r 1406  ax-ext 2000  ax-sep 3845
This theorem depends on definitions:  df-bi 110  df-tru 1229  df-nf 1326  df-sb 1624  df-clab 2005  df-cleq 2011  df-clel 2014  df-nfc 2145  df-v 2533  df-in 2897
This theorem is referenced by:  inex2  3862  inex1g  3863  inuni  3879  bnd2  3896  peano5  4244  ssimaex  5155  ofmres  5682  tfrexlem  5866
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