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Theorem bj-ru 36325
Description: Remove dependency on ax-13 2363 (and df-v 3468) from Russell's paradox ru 3769 expressed with primitive symbols and with a class variable 𝑉. Note the more economical use of elissetv 2806 instead of isset 3479 to avoid use of df-v 3468. (Contributed by BJ, 12-Oct-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-ru ¬ {𝑥 ∣ ¬ 𝑥𝑥} ∈ 𝑉

Proof of Theorem bj-ru
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 bj-ru1 36324 . 2 ¬ ∃𝑦 𝑦 = {𝑥 ∣ ¬ 𝑥𝑥}
2 elissetv 2806 . 2 ({𝑥 ∣ ¬ 𝑥𝑥} ∈ 𝑉 → ∃𝑦 𝑦 = {𝑥 ∣ ¬ 𝑥𝑥})
31, 2mto 196 1 ¬ {𝑥 ∣ ¬ 𝑥𝑥} ∈ 𝑉
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3   = wceq 1533  wex 1773  wcel 2098  {cab 2701
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-10 2129  ax-11 2146  ax-12 2163  ax-ext 2695
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-ex 1774  df-nf 1778  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802
This theorem is referenced by: (None)
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