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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-bd0el | GIF version |
Description: Boundedness of the formula "the empty set belongs to the setvar 𝑥". (Contributed by BJ, 30-Nov-2019.) |
Ref | Expression |
---|---|
bj-bd0el | ⊢ BOUNDED ∅ ∈ 𝑥 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdeq0 13054 | . 2 ⊢ BOUNDED 𝑦 = ∅ | |
2 | 1 | bj-bdcel 13024 | 1 ⊢ BOUNDED ∅ ∈ 𝑥 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1480 ∅c0 3358 BOUNDED wbd 12999 |
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-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-bd0 13000 ax-bdim 13001 ax-bdn 13004 ax-bdal 13005 ax-bdex 13006 ax-bdeq 13007 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-fal 1337 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-ral 2419 df-rex 2420 df-v 2683 df-dif 3068 df-in 3072 df-ss 3079 df-nul 3359 df-bdc 13028 |
This theorem is referenced by: bj-d0clsepcl 13112 bj-bdind 13117 |
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