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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdinex1 | Unicode version |
Description: Bounded version of inex1 4062. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bdinex1.bd | BOUNDED |
bdinex1.1 |
Ref | Expression |
---|---|
bdinex1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdinex1.1 | . . . 4 | |
2 | bdinex1.bd | . . . . . 6 BOUNDED | |
3 | 2 | bdeli 13044 | . . . . 5 BOUNDED |
4 | 3 | bdzfauscl 13088 | . . . 4 |
5 | 1, 4 | ax-mp 5 | . . 3 |
6 | dfcleq 2133 | . . . . 5 | |
7 | elin 3259 | . . . . . . 7 | |
8 | 7 | bibi2i 226 | . . . . . 6 |
9 | 8 | albii 1446 | . . . . 5 |
10 | 6, 9 | bitri 183 | . . . 4 |
11 | 10 | exbii 1584 | . . 3 |
12 | 5, 11 | mpbir 145 | . 2 |
13 | 12 | issetri 2695 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wal 1329 wceq 1331 wex 1468 wcel 1480 cvv 2686 cin 3070 BOUNDED wbdc 13038 |
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 2121 ax-bdsep 13082 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-in 3077 df-bdc 13039 |
This theorem is referenced by: bdinex2 13098 bdinex1g 13099 bdpeano5 13141 |
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