Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 1508 | . . . . . . . 8 | |
2 | bm1.1.1 | . . . . . . . 8 | |
3 | 1, 2 | nfbi 1568 | . . . . . . 7 |
4 | 3 | nfal 1555 | . . . . . 6 |
5 | elequ2 1691 | . . . . . . . 8 | |
6 | 5 | bibi1d 232 | . . . . . . 7 |
7 | 6 | albidv 1796 | . . . . . 6 |
8 | 4, 7 | sbie 1764 | . . . . 5 |
9 | 19.26 1457 | . . . . . 6 | |
10 | biantr 936 | . . . . . . . 8 | |
11 | 10 | alimi 1431 | . . . . . . 7 |
12 | ax-ext 2119 | . . . . . . 7 | |
13 | 11, 12 | syl 14 | . . . . . 6 |
14 | 9, 13 | sylbir 134 | . . . . 5 |
15 | 8, 14 | sylan2b 285 | . . . 4 |
16 | 15 | gen2 1426 | . . 3 |
17 | 16 | jctr 313 | . 2 |
18 | nfv 1508 | . . 3 | |
19 | 18 | eu2 2041 | . 2 |
20 | 17, 19 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1329 wnf 1436 wex 1468 wsb 1735 weu 1997 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 |
This theorem is referenced by: zfnuleu 4047 |
Copyright terms: Public domain | W3C validator |