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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdsepnft | Unicode version |
Description: Closed form of bdsepnf 10008. Version of ax-bdsep 10004 with one DV condition removed, the other DV condition replaced by a non-freeness antecedent, and without initial universal quantifier. Use bdsep1 10005 when sufficient. (Contributed by BJ, 19-Oct-2019.) |
Ref | Expression |
---|---|
bdsepnft.1 | BOUNDED |
Ref | Expression |
---|---|
bdsepnft |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdsepnft.1 | . . 3 BOUNDED | |
2 | 1 | bdsep2 10006 | . 2 |
3 | nfnf1 1436 | . . . 4 | |
4 | 3 | nfal 1468 | . . 3 |
5 | nfa1 1434 | . . . 4 | |
6 | nfvd 1422 | . . . . 5 | |
7 | nfv 1421 | . . . . . . 7 | |
8 | 7 | a1i 9 | . . . . . 6 |
9 | sp 1401 | . . . . . 6 | |
10 | 8, 9 | nfand 1460 | . . . . 5 |
11 | 6, 10 | nfbid 1480 | . . . 4 |
12 | 5, 11 | nfald 1643 | . . 3 |
13 | nfv 1421 | . . . . . 6 | |
14 | 5, 13 | nfan 1457 | . . . . 5 |
15 | elequ2 1601 | . . . . . . 7 | |
16 | 15 | adantl 262 | . . . . . 6 |
17 | 16 | bibi1d 222 | . . . . 5 |
18 | 14, 17 | albid 1506 | . . . 4 |
19 | 18 | ex 108 | . . 3 |
20 | 4, 12, 19 | cbvexd 1802 | . 2 |
21 | 2, 20 | mpbii 136 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wnf 1349 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-i5r 1428 ax-ext 2022 ax-bdsep 10004 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-cleq 2033 df-clel 2036 |
This theorem is referenced by: bdsepnf 10008 |
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