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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdsepnft | Unicode version |
Description: Closed form of bdsepnf 13075. Version of ax-bdsep 13071 with one disjoint variable condition removed, the other disjoint variable condition replaced by a non-freeness antecedent, and without initial universal quantifier. Use bdsep1 13072 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 13073 | . 2 |
3 | nfnf1 1523 | . . . 4 | |
4 | 3 | nfal 1555 | . . 3 |
5 | nfa1 1521 | . . . 4 | |
6 | nfvd 1509 | . . . . 5 | |
7 | nfv 1508 | . . . . . . 7 | |
8 | 7 | a1i 9 | . . . . . 6 |
9 | sp 1488 | . . . . . 6 | |
10 | 8, 9 | nfand 1547 | . . . . 5 |
11 | 6, 10 | nfbid 1567 | . . . 4 |
12 | 5, 11 | nfald 1733 | . . 3 |
13 | nfv 1508 | . . . . . 6 | |
14 | 5, 13 | nfan 1544 | . . . . 5 |
15 | elequ2 1691 | . . . . . . 7 | |
16 | 15 | adantl 275 | . . . . . 6 |
17 | 16 | bibi1d 232 | . . . . 5 |
18 | 14, 17 | albid 1594 | . . . 4 |
19 | 18 | ex 114 | . . 3 |
20 | 4, 12, 19 | cbvexd 1897 | . 2 |
21 | 2, 20 | mpbii 147 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wnf 1436 wex 1468 BOUNDED wbd 12999 |
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 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-bdsep 13071 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-cleq 2130 df-clel 2133 |
This theorem is referenced by: bdsepnf 13075 |
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