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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 2162 to strengthen the hypothesis in the form of axnul 4125). (Contributed by NM, 22-Dec-2007.) |
Ref | Expression |
---|---|
zfnuleu.1 |
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Ref | Expression |
---|---|
zfnuleu |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | zfnuleu.1 |
. . . 4
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2 | nbfal 1364 |
. . . . . 6
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3 | 2 | albii 1470 |
. . . . 5
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4 | 3 | exbii 1605 |
. . . 4
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5 | 1, 4 | mpbi 145 |
. . 3
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6 | nfv 1528 |
. . . 4
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7 | 6 | bm1.1 2162 |
. . 3
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8 | 5, 7 | ax-mp 5 |
. 2
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9 | 3 | eubii 2035 |
. 2
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10 | 8, 9 | mpbir 146 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 |
This theorem is referenced by: (None) |
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