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Mirrors > Home > ILE Home > Th. List > sndisj | Unicode version |
Description: Any collection of singletons is disjoint. (Contributed by Mario Carneiro, 14-Nov-2016.) |
Ref | Expression |
---|---|
sndisj |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfdisj2 3776 |
. 2
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2 | moeq 2768 |
. . 3
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3 | simpr 108 |
. . . . . 6
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4 | velsn 3423 |
. . . . . 6
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5 | 3, 4 | sylib 120 |
. . . . 5
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6 | 5 | eqcomd 2087 |
. . . 4
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7 | 6 | moimi 2007 |
. . 3
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8 | 2, 7 | ax-mp 7 |
. 2
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9 | 1, 8 | mpgbir 1383 |
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 104 ax-ia2 105 ax-ia3 106 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2064 |
This theorem depends on definitions: df-bi 115 df-tru 1288 df-nf 1391 df-sb 1687 df-eu 1945 df-mo 1946 df-clab 2069 df-cleq 2075 df-clel 2078 df-nfc 2209 df-rmo 2357 df-v 2604 df-sn 3412 df-disj 3775 |
This theorem is referenced by: 0disj 3790 |
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