Mathbox for BJ |
< Previous
Next >
Nearby theorems |
||
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 13068 | . 2 ⊢ BOUNDED 𝑧 = suc 𝑥 | |
2 | 1 | bj-bdcel 13024 | 1 ⊢ BOUNDED suc 𝑥 ∈ 𝑦 |
Colors of variables: wff set class |
Syntax hints: ∈ wcel 1480 suc csuc 4282 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-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-bdan 13002 ax-bdor 13003 ax-bdal 13005 ax-bdex 13006 ax-bdeq 13007 ax-bdel 13008 ax-bdsb 13009 |
This theorem depends on definitions: df-bi 116 df-tru 1334 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-un 3070 df-in 3072 df-ss 3079 df-sn 3528 df-suc 4288 df-bdc 13028 |
This theorem is referenced by: bj-bdind 13117 |
Copyright terms: Public domain | W3C validator |