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Theorem ralndv1 47117
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 9636 . . 3 ¬ 𝑥𝑥
21pm2.21i 119 . 2 (𝑥𝑥 → V ∈ 𝑥)
32rgen 3063 1 𝑥𝑥 V ∈ 𝑥
Colors of variables: wff setvar class
Syntax hints:  wcel 2108  wral 3061  Vcvv 3480
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-10 2141  ax-12 2177  ax-ext 2708  ax-sep 5296  ax-pr 5432  ax-reg 9632
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-ex 1780  df-nf 1784  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-ral 3062  df-rex 3071  df-v 3482  df-un 3956  df-sn 4627  df-pr 4629
This theorem is referenced by: (None)
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