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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 15072 | . 2 ⊢ BOUNDED 𝑦 = ∅ | |
2 | 1 | bj-bdcel 15042 | 1 ⊢ BOUNDED ∅ ∈ 𝑥 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2160 ∅c0 3437 BOUNDED wbd 15017 |
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-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 ax-bd0 15018 ax-bdim 15019 ax-bdn 15022 ax-bdal 15023 ax-bdex 15024 ax-bdeq 15025 |
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-nfc 2321 df-ral 2473 df-rex 2474 df-v 2754 df-dif 3146 df-in 3150 df-ss 3157 df-nul 3438 df-bdc 15046 |
This theorem is referenced by: bj-d0clsepcl 15130 bj-bdind 15135 |
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