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Theorem axsep2 3904
 Description: A less restrictive version of the Separation Scheme ax-sep 3903, where variables and can both appear free in the wff , which can therefore be thought of as . This version was derived from the more restrictive ax-sep 3903 with no additional set theory axioms. (Contributed by NM, 10-Dec-2006.) (Proof shortened by Mario Carneiro, 17-Nov-2016.)
Assertion
Ref Expression
axsep2
Distinct variable groups:   ,,   ,
Allowed substitution hints:   (,)

Proof of Theorem axsep2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq2 2117 . . . . . . 7
21anbi1d 446 . . . . . 6
3 anabs5 515 . . . . . 6
42, 3syl6bb 189 . . . . 5
54bibi2d 225 . . . 4
65albidv 1721 . . 3
76exbidv 1722 . 2
8 ax-sep 3903 . 2
97, 8chvarv 1828 1
 Colors of variables: wff set class Syntax hints:   wa 101   wb 102  wal 1257  wex 1397 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-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-cleq 2049  df-clel 2052 This theorem is referenced by: (None)
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