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Mirrors > Home > ILE Home > Th. List > eqeu | Unicode version |
Description: A condition which implies existential uniqueness. (Contributed by Jeff Hankins, 8-Sep-2009.) |
Ref | Expression |
---|---|
eqeu.1 |
Ref | Expression |
---|---|
eqeu |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeu.1 | . . . . 5 | |
2 | 1 | spcegv 2769 | . . . 4 |
3 | 2 | imp 123 | . . 3 |
4 | 3 | 3adant3 1001 | . 2 |
5 | eqeq2 2147 | . . . . . . 7 | |
6 | 5 | imbi2d 229 | . . . . . 6 |
7 | 6 | albidv 1796 | . . . . 5 |
8 | 7 | spcegv 2769 | . . . 4 |
9 | 8 | imp 123 | . . 3 |
10 | 9 | 3adant2 1000 | . 2 |
11 | nfv 1508 | . . 3 | |
12 | 11 | eu3 2043 | . 2 |
13 | 4, 10, 12 | sylanbrc 413 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 w3a 962 wal 1329 wceq 1331 wex 1468 wcel 1480 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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-eu 2000 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 |
This theorem is referenced by: (None) |
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