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Mirrors > Home > ILE Home > Th. List > nssne2 | Unicode version |
Description: Two classes are different if they are not subclasses of the same class. (Contributed by NM, 23-Apr-2015.) |
Ref | Expression |
---|---|
nssne2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sseq1 3147 |
. . . 4
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2 | 1 | biimpcd 158 |
. . 3
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3 | 2 | necon3bd 2367 |
. 2
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4 | 3 | imp 123 |
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-in1 604 ax-in2 605 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1481 ax-11 1483 ax-4 1487 ax-17 1503 ax-i9 1507 ax-ial 1511 ax-i5r 1512 ax-ext 2136 |
This theorem depends on definitions: df-bi 116 df-nf 1438 df-sb 1740 df-clab 2141 df-cleq 2147 df-clel 2150 df-ne 2325 df-in 3104 df-ss 3111 |
This theorem is referenced by: (None) |
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