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Mirrors > Home > ILE Home > Th. List > ssneld | Unicode version |
Description: If a class is not in another class, it is also not in a subclass of that class. Deduction form. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
ssneld.1 |
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Ref | Expression |
---|---|
ssneld |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssneld.1 |
. . 3
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2 | 1 | sseld 3027 |
. 2
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3 | 2 | con3d 597 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 580 ax-in2 581 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-11 1443 ax-4 1446 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 |
This theorem depends on definitions: df-bi 116 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-in 3008 df-ss 3015 |
This theorem is referenced by: ssneldd 3031 sumdc 10810 isummolem2a 10834 zisum 10837 isumss2 10848 decidin 12001 |
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