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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 14904 | . 2 ⊢ BOUNDED 𝑧 = suc 𝑥 | |
2 | 1 | bj-bdcel 14860 | 1 ⊢ BOUNDED suc 𝑥 ∈ 𝑦 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 2158 suc csuc 4377 BOUNDED wbd 14835 |
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-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-ext 2169 ax-bd0 14836 ax-bdan 14838 ax-bdor 14839 ax-bdal 14841 ax-bdex 14842 ax-bdeq 14843 ax-bdel 14844 ax-bdsb 14845 |
This theorem depends on definitions: df-bi 117 df-tru 1366 df-nf 1471 df-sb 1773 df-clab 2174 df-cleq 2180 df-clel 2183 df-nfc 2318 df-ral 2470 df-rex 2471 df-v 2751 df-un 3145 df-in 3147 df-ss 3154 df-sn 3610 df-suc 4383 df-bdc 14864 |
This theorem is referenced by: bj-bdind 14953 |
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