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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-bdsucel | GIF version |
Description: Boundedness of the formula "the successor of the setvar 𝑥 belongs to the setvar 𝑦". (Contributed by BJ, 30-Nov-2019.) |
Ref | Expression |
---|---|
bj-bdsucel | ⊢ BOUNDED suc 𝑥 ∈ 𝑦 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdeqsuc 13876 | . 2 ⊢ BOUNDED 𝑧 = suc 𝑥 | |
2 | 1 | bj-bdcel 13832 | 1 ⊢ BOUNDED suc 𝑥 ∈ 𝑦 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2141 suc csuc 4348 BOUNDED wbd 13807 |
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-io 704 ax-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-10 1498 ax-11 1499 ax-i12 1500 ax-bndl 1502 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 ax-bd0 13808 ax-bdan 13810 ax-bdor 13811 ax-bdal 13813 ax-bdex 13814 ax-bdeq 13815 ax-bdel 13816 ax-bdsb 13817 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 df-clel 2166 df-nfc 2301 df-ral 2453 df-rex 2454 df-v 2732 df-un 3125 df-in 3127 df-ss 3134 df-sn 3587 df-suc 4354 df-bdc 13836 |
This theorem is referenced by: bj-bdind 13925 |
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