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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdsepnft | Unicode version |
Description: Closed form of bdsepnf 13883. Version of ax-bdsep 13879 with one disjoint variable condition removed, the other disjoint variable condition replaced by a nonfreeness antecedent, and without initial universal quantifier. Use bdsep1 13880 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 13881 | . 2 |
3 | nfnf1 1537 | . . . 4 | |
4 | 3 | nfal 1569 | . . 3 |
5 | nfa1 1534 | . . . 4 | |
6 | nfvd 1522 | . . . . 5 | |
7 | nfv 1521 | . . . . . . 7 | |
8 | 7 | a1i 9 | . . . . . 6 |
9 | sp 1504 | . . . . . 6 | |
10 | 8, 9 | nfand 1561 | . . . . 5 |
11 | 6, 10 | nfbid 1581 | . . . 4 |
12 | 5, 11 | nfald 1753 | . . 3 |
13 | nfv 1521 | . . . . . 6 | |
14 | 5, 13 | nfan 1558 | . . . . 5 |
15 | elequ2 2146 | . . . . . . 7 | |
16 | 15 | adantl 275 | . . . . . 6 |
17 | 16 | bibi1d 232 | . . . . 5 |
18 | 14, 17 | albid 1608 | . . . 4 |
19 | 18 | ex 114 | . . 3 |
20 | 4, 12, 19 | cbvexd 1920 | . 2 |
21 | 2, 20 | mpbii 147 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1346 wnf 1453 wex 1485 BOUNDED wbd 13807 |
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-5 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-14 2144 ax-ext 2152 ax-bdsep 13879 |
This theorem depends on definitions: df-bi 116 df-nf 1454 df-cleq 2163 df-clel 2166 |
This theorem is referenced by: bdsepnf 13883 |
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