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Theorem inex1 3891
 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
Assertion
Ref Expression
inex1

Proof of Theorem inex1
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 inex1.1 . . . 4
21zfauscl 3877 . . 3
3 dfcleq 2034 . . . . 5
4 elin 3126 . . . . . . 7
54bibi2i 216 . . . . . 6
65albii 1359 . . . . 5
73, 6bitri 173 . . . 4
87exbii 1496 . . 3
92, 8mpbir 134 . 2
109issetri 2564 1
 Colors of variables: wff set class Syntax hints:   wa 97   wb 98  wal 1241   wceq 1243  wex 1381   wcel 1393  cvv 2557   cin 2916 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924 This theorem is referenced by:  inex2  3892  inex1g  3893  inuni  3909  bnd2  3926  peano5  4321  ssimaex  5234  ofmres  5763  tfrexlem  5948
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