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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 1461 | . . . . . . . 8 | |
2 | bm1.1.1 | . . . . . . . 8 | |
3 | 1, 2 | nfbi 1521 | . . . . . . 7 |
4 | 3 | nfal 1508 | . . . . . 6 |
5 | elequ2 1641 | . . . . . . . 8 | |
6 | 5 | bibi1d 231 | . . . . . . 7 |
7 | 6 | albidv 1745 | . . . . . 6 |
8 | 4, 7 | sbie 1714 | . . . . 5 |
9 | 19.26 1410 | . . . . . 6 | |
10 | biantr 893 | . . . . . . . 8 | |
11 | 10 | alimi 1384 | . . . . . . 7 |
12 | ax-ext 2063 | . . . . . . 7 | |
13 | 11, 12 | syl 14 | . . . . . 6 |
14 | 9, 13 | sylbir 133 | . . . . 5 |
15 | 8, 14 | sylan2b 281 | . . . 4 |
16 | 15 | gen2 1379 | . . 3 |
17 | 16 | jctr 308 | . 2 |
18 | nfv 1461 | . . 3 | |
19 | 18 | eu2 1985 | . 2 |
20 | 17, 19 | sylibr 132 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wnf 1389 wex 1421 wsb 1685 weu 1941 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 |
This theorem is referenced by: zfnuleu 3902 |
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