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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 2022 to strengthen the hypothesis in the form of axnul 3873). (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 1253 |
. . . . . 6
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3 | 2 | albii 1356 |
. . . . 5
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4 | 3 | exbii 1493 |
. . . 4
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5 | 1, 4 | mpbi 133 |
. . 3
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6 | nfv 1418 |
. . . 4
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7 | 6 | bm1.1 2022 |
. . 3
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8 | 5, 7 | ax-mp 7 |
. 2
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9 | 3 | eubii 1906 |
. 2
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10 | 8, 9 | mpbir 134 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-bndl 1396 ax-4 1397 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-fal 1248 df-nf 1347 df-sb 1643 df-eu 1900 |
This theorem is referenced by: (None) |
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