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Mirrors > Home > ILE Home > Th. List > neleqtrd | Unicode version |
Description: If a class is not an element of another class, it is also not an element of an equal class. Deduction form. (Contributed by David Moews, 1-May-2017.) |
Ref | Expression |
---|---|
neleqtrd.1 |
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neleqtrd.2 |
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Ref | Expression |
---|---|
neleqtrd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | neleqtrd.1 |
. 2
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2 | neleqtrd.2 |
. . 3
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3 | 2 | eleq2d 2257 |
. 2
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4 | 1, 3 | mtbid 673 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-5 1457 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-4 1520 ax-17 1536 ax-ial 1544 ax-ext 2169 |
This theorem depends on definitions: df-bi 117 df-cleq 2180 df-clel 2183 |
This theorem is referenced by: (None) |
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