Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-vnex | GIF version |
Description: vnex 4059 from bounded separation. (Contributed by BJ, 18-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bj-vnex | ⊢ ¬ ∃𝑥 𝑥 = V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-vprc 13099 | . 2 ⊢ ¬ V ∈ V | |
2 | isset 2692 | . 2 ⊢ (V ∈ V ↔ ∃𝑥 𝑥 = V) | |
3 | 1, 2 | mtbi 659 | 1 ⊢ ¬ ∃𝑥 𝑥 = V |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 = wceq 1331 ∃wex 1468 ∈ wcel 1480 Vcvv 2686 |
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 13020 ax-bdel 13024 ax-bdsep 13087 |
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) |
Copyright terms: Public domain | W3C validator |