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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 1493 | . . . . . . . 8 | |
2 | bm1.1.1 | . . . . . . . 8 | |
3 | 1, 2 | nfbi 1553 | . . . . . . 7 |
4 | 3 | nfal 1540 | . . . . . 6 |
5 | elequ2 1676 | . . . . . . . 8 | |
6 | 5 | bibi1d 232 | . . . . . . 7 |
7 | 6 | albidv 1780 | . . . . . 6 |
8 | 4, 7 | sbie 1749 | . . . . 5 |
9 | 19.26 1442 | . . . . . 6 | |
10 | biantr 921 | . . . . . . . 8 | |
11 | 10 | alimi 1416 | . . . . . . 7 |
12 | ax-ext 2099 | . . . . . . 7 | |
13 | 11, 12 | syl 14 | . . . . . 6 |
14 | 9, 13 | sylbir 134 | . . . . 5 |
15 | 8, 14 | sylan2b 285 | . . . 4 |
16 | 15 | gen2 1411 | . . 3 |
17 | 16 | jctr 313 | . 2 |
18 | nfv 1493 | . . 3 | |
19 | 18 | eu2 2021 | . 2 |
20 | 17, 19 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1314 wnf 1421 wex 1453 wsb 1720 weu 1977 |
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-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 |
This theorem is referenced by: zfnuleu 4022 |
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