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Theorem zfauscl 3905
 Description: Separation Scheme (Aussonderung) using a class variable. To derive this from ax-sep 3903, we invoke the Axiom of Extensionality (indirectly via vtocl 2625), which is needed for the justification of class variable notation. (Contributed by NM, 5-Aug-1993.)
Hypothesis
Ref Expression
zfauscl.1
Assertion
Ref Expression
zfauscl
Distinct variable groups:   ,,   ,
Allowed substitution hint:   ()

Proof of Theorem zfauscl
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 zfauscl.1 . 2
2 eleq2 2117 . . . . . 6
32anbi1d 446 . . . . 5
43bibi2d 225 . . . 4
54albidv 1721 . . 3
65exbidv 1722 . 2
7 ax-sep 3903 . 2
81, 6, 7vtocl 2625 1
 Colors of variables: wff set class Syntax hints:   wa 101   wb 102  wal 1257   wceq 1259  wex 1397   wcel 1409  cvv 2574 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-ext 2038  ax-sep 3903 This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-v 2576 This theorem is referenced by:  inex1  3919  bj-d0clsepcl  10436
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