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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 3916 |
. 2
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2 | moeq 2863 |
. . 3
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3 | simpr 109 |
. . . . . 6
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4 | velsn 3549 |
. . . . . 6
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5 | 3, 4 | sylib 121 |
. . . . 5
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6 | 5 | eqcomd 2146 |
. . . 4
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7 | 6 | moimi 2065 |
. . 3
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8 | 2, 7 | ax-mp 5 |
. 2
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9 | 1, 8 | mpgbir 1430 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rmo 2425 df-v 2691 df-sn 3538 df-disj 3915 |
This theorem is referenced by: 0disj 3934 disjsnxp 6142 |
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