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Theorem ralndv1 45423
Description: Example for a theorem about a restricted universal quantification in which the restricting class depends on (actually is) the bound variable: All sets containing themselves contain the universal class. (Contributed by AV, 24-Jun-2023.)
Assertion
Ref Expression
ralndv1 𝑥𝑥 V ∈ 𝑥

Proof of Theorem ralndv1
StepHypRef Expression
1 elirrv 9537 . . 3 ¬ 𝑥𝑥
21pm2.21i 119 . 2 (𝑥𝑥 → V ∈ 𝑥)
32rgen 3063 1 𝑥𝑥 V ∈ 𝑥
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  wral 3061  Vcvv 3444
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-12 2172  ax-ext 2704  ax-sep 5257  ax-pr 5385  ax-reg 9533
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-nf 1787  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ral 3062  df-rex 3071  df-v 3446  df-un 3916  df-sn 4588  df-pr 4590
This theorem is referenced by: (None)
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