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Mirrors > Home > ILE Home > Th. List > bm1.1 | Unicode version |
Description: Any set defined by a property is the only set defined by that property. Theorem 1.1 of [BellMachover] p. 462. (Contributed by NM, 30-Jun-1994.) |
Ref | Expression |
---|---|
bm1.1.1 |
Ref | Expression |
---|---|
bm1.1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1421 | . . . . . . . 8 | |
2 | bm1.1.1 | . . . . . . . 8 | |
3 | 1, 2 | nfbi 1481 | . . . . . . 7 |
4 | 3 | nfal 1468 | . . . . . 6 |
5 | elequ2 1601 | . . . . . . . 8 | |
6 | 5 | bibi1d 222 | . . . . . . 7 |
7 | 6 | albidv 1705 | . . . . . 6 |
8 | 4, 7 | sbie 1674 | . . . . 5 |
9 | 19.26 1370 | . . . . . 6 | |
10 | biantr 859 | . . . . . . . 8 | |
11 | 10 | alimi 1344 | . . . . . . 7 |
12 | ax-ext 2022 | . . . . . . 7 | |
13 | 11, 12 | syl 14 | . . . . . 6 |
14 | 9, 13 | sylbir 125 | . . . . 5 |
15 | 8, 14 | sylan2b 271 | . . . 4 |
16 | 15 | gen2 1339 | . . 3 |
17 | 16 | jctr 298 | . 2 |
18 | nfv 1421 | . . 3 | |
19 | 18 | eu2 1944 | . 2 |
20 | 17, 19 | sylibr 137 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wb 98 wal 1241 wnf 1349 wex 1381 wsb 1645 weu 1900 |
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-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-eu 1903 |
This theorem is referenced by: zfnuleu 3881 |
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