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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-intnexr | GIF version |
Description: intnexr 4076 from bounded separation. (Contributed by BJ, 18-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-intnexr | ⊢ (∩ 𝐴 = V → ¬ ∩ 𝐴 ∈ V) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-vprc 13094 | . 2 ⊢ ¬ V ∈ V | |
2 | eleq1 2202 | . 2 ⊢ (∩ 𝐴 = V → (∩ 𝐴 ∈ V ↔ V ∈ V)) | |
3 | 1, 2 | mtbiri 664 | 1 ⊢ (∩ 𝐴 = V → ¬ ∩ 𝐴 ∈ V) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 = wceq 1331 ∈ wcel 1480 Vcvv 2686 ∩ cint 3771 |
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 603 ax-in2 604 ax-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-ext 2121 ax-bdn 13015 ax-bdel 13019 ax-bdsep 13082 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-v 2688 |
This theorem is referenced by: (None) |
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