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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 3470 | . 2 ⊢ (𝐴 = V ↔ ∀𝑥 𝑥 ∈ 𝐴) | |
2 | 1 | necon3abii 2976 | 1 ⊢ (𝐴 ≠ V ↔ ¬ ∀𝑥 𝑥 ∈ 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 205 ∀wal 1531 ∈ wcel 2098 ≠ wne 2929 Vcvv 3461 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2696 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2703 df-cleq 2717 df-clel 2802 df-ne 2930 df-v 3463 |
This theorem is referenced by: (None) |
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