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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-nvel | GIF version |
Description: nvel 4031 from bounded separation. (Contributed by BJ, 18-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-nvel | ⊢ ¬ V ∈ 𝐴 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-vprc 13021 | . 2 ⊢ ¬ V ∈ V | |
2 | elex 2671 | . 2 ⊢ (V ∈ 𝐴 → V ∈ V) | |
3 | 1, 2 | mto 636 | 1 ⊢ ¬ V ∈ 𝐴 |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∈ wcel 1465 Vcvv 2660 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 588 ax-in2 589 ax-5 1408 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-ext 2099 ax-bdn 12942 ax-bdel 12946 ax-bdsep 13009 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-fal 1322 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-v 2662 |
This theorem is referenced by: (None) |
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