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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdbm1.3ii | Unicode version |
Description: Bounded version of bm1.3ii 3878. (Contributed by BJ, 5-Oct-2019.) (Proof modification is discouraged.) |
Ref | Expression |
---|---|
bdbm1.3ii.bd | BOUNDED |
bdbm1.3ii.1 |
Ref | Expression |
---|---|
bdbm1.3ii |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdbm1.3ii.1 | . . . . 5 | |
2 | elequ2 1601 | . . . . . . . 8 | |
3 | 2 | imbi2d 219 | . . . . . . 7 |
4 | 3 | albidv 1705 | . . . . . 6 |
5 | 4 | cbvexv 1795 | . . . . 5 |
6 | 1, 5 | mpbi 133 | . . . 4 |
7 | bdbm1.3ii.bd | . . . . 5 BOUNDED | |
8 | 7 | bdsep1 10005 | . . . 4 |
9 | 6, 8 | pm3.2i 257 | . . 3 |
10 | 9 | exan 1583 | . 2 |
11 | 19.42v 1786 | . . . 4 | |
12 | bimsc1 870 | . . . . . 6 | |
13 | 12 | alanimi 1348 | . . . . 5 |
14 | 13 | eximi 1491 | . . . 4 |
15 | 11, 14 | sylbir 125 | . . 3 |
16 | 15 | exlimiv 1489 | . 2 |
17 | 10, 16 | ax-mp 7 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wex 1381 BOUNDED wbd 9932 |
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-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-bdsep 10004 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: bj-zfpair2 10030 bj-axun2 10035 bj-uniex2 10036 |
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