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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 3449 | . 2 ⊢ (𝐴 = V ↔ ∀𝑥 𝑥 ∈ 𝐴) | |
2 | 1 | necon3abii 3033 | 1 ⊢ (𝐴 ≠ V ↔ ¬ ∀𝑥 𝑥 ∈ 𝐴) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ↔ wb 209 ∀wal 1536 ∈ wcel 2111 ≠ wne 2987 Vcvv 3441 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1911 ax-6 1970 ax-7 2015 ax-8 2113 ax-9 2121 ax-ext 2770 |
This theorem depends on definitions: df-bi 210 df-an 400 df-ex 1782 df-sb 2070 df-clab 2777 df-cleq 2791 df-clel 2870 df-ne 2988 df-v 3443 |
This theorem is referenced by: (None) |
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