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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdinex1 | Unicode version |
Description: Bounded version of inex1 3891. (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 9966 | . . . . 5 BOUNDED |
4 | 3 | bdzfauscl 10010 | . . . 4 |
5 | 1, 4 | ax-mp 7 | . . 3 |
6 | dfcleq 2034 | . . . . 5 | |
7 | elin 3126 | . . . . . . 7 | |
8 | 7 | bibi2i 216 | . . . . . 6 |
9 | 8 | albii 1359 | . . . . 5 |
10 | 6, 9 | bitri 173 | . . . 4 |
11 | 10 | exbii 1496 | . . 3 |
12 | 5, 11 | mpbir 134 | . 2 |
13 | 12 | issetri 2564 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 97 wb 98 wal 1241 wceq 1243 wex 1381 wcel 1393 cvv 2557 cin 2916 BOUNDED wbdc 9960 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-bdsep 10004 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-in 2924 df-bdc 9961 |
This theorem is referenced by: bdinex2 10020 bdinex1g 10021 bdpeano5 10068 |
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