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Theorem bj-ru 31583
Description: Remove dependency on ax-13 2101 (and df-v 3058) from Russell's paradox ru 3277 expressed with primitive symbols and with a class variable  V (note that axsep2 4539 does require ax-8 1899 and ax-9 1906 since it requires df-clel 2457 and df-cleq 2454--- see bj-df-clel 31540 and bj-df-cleq 31544). Note the more economical use of bj-elissetv 31514 instead of isset 3060 to avoid use of df-v 3058. (Contributed by BJ, 12-Oct-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-ru  |-  -.  {
x  |  -.  x  e.  x }  e.  V

Proof of Theorem bj-ru
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 bj-ru1 31582 . 2  |-  -.  E. y  y  =  {
x  |  -.  x  e.  x }
2 bj-elissetv 31514 . 2  |-  ( { x  |  -.  x  e.  x }  e.  V  ->  E. y  y  =  { x  |  -.  x  e.  x }
)
31, 2mto 181 1  |-  -.  {
x  |  -.  x  e.  x }  e.  V
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    = wceq 1454   E.wex 1673    e. wcel 1897   {cab 2447
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-8 1899  ax-9 1906  ax-10 1925  ax-11 1930  ax-12 1943  ax-ext 2441
This theorem depends on definitions:  df-bi 190  df-an 377  df-tru 1457  df-ex 1674  df-nf 1678  df-sb 1808  df-clab 2448  df-cleq 2454  df-clel 2457
This theorem is referenced by: (None)
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