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Theorem ralndv2 45424
Description: Second example for a theorem about a restricted universal quantification in which the restricting class depends on the bound variable: all subsets of a set are sets. (Contributed by AV, 24-Jun-2023.)
Assertion
Ref Expression
ralndv2 𝑥 ∈ 𝒫 𝑥𝑥 ∈ V

Proof of Theorem ralndv2
StepHypRef Expression
1 vex 3448 . 2 𝑥 ∈ V
21rgenw 3065 1 𝑥 ∈ 𝒫 𝑥𝑥 ∈ V
Colors of variables: wff setvar class
Syntax hints:  wcel 2107  wral 3061  Vcvv 3444  𝒫 cpw 4561
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-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ral 3062  df-v 3446
This theorem is referenced by: (None)
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