Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > absneu | Unicode version |
Description: Restricted existential uniqueness determined by a singleton. (Contributed by NM, 29-May-2006.) |
Ref | Expression |
---|---|
absneu |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sneq 3508 | . . . . 5 | |
2 | 1 | eqeq2d 2129 | . . . 4 |
3 | 2 | spcegv 2748 | . . 3 |
4 | 3 | imp 123 | . 2 |
5 | euabsn2 3562 | . 2 | |
6 | 4, 5 | sylibr 133 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wceq 1316 wex 1453 wcel 1465 weu 1977 cab 2103 csn 3497 |
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-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 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-sn 3503 |
This theorem is referenced by: rabsneu 3566 |
Copyright terms: Public domain | W3C validator |