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Mirrors > Home > ILE Home > Th. List > zfnuleu | Unicode version |
Description: Show the uniqueness of the empty set (using the Axiom of Extensionality via bm1.1 2122 to strengthen the hypothesis in the form of axnul 4048). (Contributed by NM, 22-Dec-2007.) |
Ref | Expression |
---|---|
zfnuleu.1 |
Ref | Expression |
---|---|
zfnuleu |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zfnuleu.1 | . . . 4 | |
2 | nbfal 1342 | . . . . . 6 | |
3 | 2 | albii 1446 | . . . . 5 |
4 | 3 | exbii 1584 | . . . 4 |
5 | 1, 4 | mpbi 144 | . . 3 |
6 | nfv 1508 | . . . 4 | |
7 | 6 | bm1.1 2122 | . . 3 |
8 | 5, 7 | ax-mp 5 | . 2 |
9 | 3 | eubii 2006 | . 2 |
10 | 8, 9 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wb 104 wal 1329 wfal 1336 wex 1468 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-in1 603 ax-in2 604 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-fal 1337 df-nf 1437 df-sb 1736 df-eu 2000 |
This theorem is referenced by: (None) |
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