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Mirrors > Home > ILE Home > Th. List > nfabdw | Unicode version |
Description: Bound-variable hypothesis builder for a class abstraction. Version of nfabd 2319 with a disjoint variable condition. (Contributed by Mario Carneiro, 8-Oct-2016.) (Revised by Gino Giotto, 10-Jan-2024.) |
Ref | Expression |
---|---|
nfabdw.1 | |
nfabdw.2 |
Ref | Expression |
---|---|
nfabdw |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1508 | . 2 | |
2 | df-clab 2144 | . . 3 | |
3 | nfabdw.1 | . . . . 5 | |
4 | nfabdw.2 | . . . . 5 | |
5 | 3, 4 | alrimi 1502 | . . . 4 |
6 | nfa1 1521 | . . . . . . . . 9 | |
7 | sb6 1866 | . . . . . . . . . . . 12 | |
8 | 7 | a1i 9 | . . . . . . . . . . 11 |
9 | 7 | biimpri 132 | . . . . . . . . . . . 12 |
10 | 9 | axc4i 1522 | . . . . . . . . . . 11 |
11 | 8, 10 | syl6bi 162 | . . . . . . . . . 10 |
12 | 6, 11 | nf5d 2005 | . . . . . . . . 9 |
13 | 6, 12 | nfim1 1551 | . . . . . . . 8 |
14 | sbequ12 1751 | . . . . . . . . 9 | |
15 | 14 | imbi2d 229 | . . . . . . . 8 |
16 | 13, 15 | equsalv 1773 | . . . . . . 7 |
17 | 16 | bicomi 131 | . . . . . 6 |
18 | nfv 1508 | . . . . . . . 8 | |
19 | nfnf1 1524 | . . . . . . . . . 10 | |
20 | 19 | nfal 1556 | . . . . . . . . 9 |
21 | sp 1491 | . . . . . . . . 9 | |
22 | 20, 21 | nfim1 1551 | . . . . . . . 8 |
23 | 18, 22 | nfim 1552 | . . . . . . 7 |
24 | 23 | nfal 1556 | . . . . . 6 |
25 | 17, 24 | nfxfr 1454 | . . . . 5 |
26 | pm5.5 241 | . . . . . 6 | |
27 | 20, 26 | nfbidf 1519 | . . . . 5 |
28 | 25, 27 | mpbii 147 | . . . 4 |
29 | 5, 28 | syl 14 | . . 3 |
30 | 2, 29 | nfxfrd 1455 | . 2 |
31 | 1, 30 | nfcd 2294 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1333 wnf 1440 wsb 1742 wcel 2128 cab 2143 wnfc 2286 |
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 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-11 1486 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 |
This theorem depends on definitions: df-bi 116 df-nf 1441 df-sb 1743 df-clab 2144 df-nfc 2288 |
This theorem is referenced by: nfsbcdw 3065 nfcsbw 3067 |
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