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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-intnexr | GIF version |
Description: intnexr 4169 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 15106 | . 2 ⊢ ¬ V ∈ V | |
2 | eleq1 2252 | . 2 ⊢ (∩ 𝐴 = V → (∩ 𝐴 ∈ V ↔ V ∈ V)) | |
3 | 1, 2 | mtbiri 676 | 1 ⊢ (∩ 𝐴 = V → ¬ ∩ 𝐴 ∈ V) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 = wceq 1364 ∈ wcel 2160 Vcvv 2752 ∩ cint 3859 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-5 1458 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-13 2162 ax-14 2163 ax-ext 2171 ax-bdn 15027 ax-bdel 15031 ax-bdsep 15094 |
This theorem depends on definitions: df-bi 117 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-v 2754 |
This theorem is referenced by: (None) |
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