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Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > ralndv1 | Structured version Visualization version GIF version |
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.) |
Ref | Expression |
---|---|
ralndv1 | ⊢ ∀𝑥 ∈ 𝑥 V ∈ 𝑥 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elirrv 9633 | . . 3 ⊢ ¬ 𝑥 ∈ 𝑥 | |
2 | 1 | pm2.21i 119 | . 2 ⊢ (𝑥 ∈ 𝑥 → V ∈ 𝑥) |
3 | 2 | rgen 3060 | 1 ⊢ ∀𝑥 ∈ 𝑥 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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