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Mirrors > Home > MPE Home > Th. List > Mathboxes > nev | Structured version Visualization version GIF version |
Description: Express that not every set is in a class. (Contributed by RP, 16-Apr-2020.) |
Ref | Expression |
---|---|
nev | ⊢ (𝐴 ≠ V ↔ ¬ ∀𝑥 𝑥 ∈ 𝐴) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqv 3404 | . 2 ⊢ (𝐴 = V ↔ ∀𝑥 𝑥 ∈ 𝐴) | |
2 | 1 | necon3abii 3014 | 1 ⊢ (𝐴 ≠ V ↔ ¬ ∀𝑥 𝑥 ∈ 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 198 ∀wal 1599 ∈ wcel 2106 ≠ wne 2968 Vcvv 3397 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2054 ax-9 2115 ax-12 2162 ax-ext 2753 |
This theorem depends on definitions: df-bi 199 df-an 387 df-tru 1605 df-ex 1824 df-sb 2012 df-clab 2763 df-cleq 2769 df-clel 2773 df-ne 2969 df-v 3399 |
This theorem is referenced by: (None) |
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