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Theorem ralndv1 47054
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 9633 . . 3 ¬ 𝑥𝑥
21pm2.21i 119 . 2 (𝑥𝑥 → V ∈ 𝑥)
32rgen 3060 1 𝑥𝑥 V ∈ 𝑥
Colors of variables: wff setvar class
Syntax hints:  wcel 2105  wral 3058  Vcvv 3477
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004  ax-8 2107  ax-9 2115  ax-10 2138  ax-12 2174  ax-ext 2705  ax-sep 5301  ax-pr 5437  ax-reg 9629
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1539  df-ex 1776  df-nf 1780  df-sb 2062  df-clab 2712  df-cleq 2726  df-clel 2813  df-ral 3059  df-rex 3068  df-v 3479  df-un 3967  df-sn 4631  df-pr 4633
This theorem is referenced by: (None)
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