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Mirrors > Home > ILE Home > Th. List > neleq1 | Unicode version |
Description: Equality theorem for negated membership. (Contributed by NM, 20-Nov-1994.) |
Ref | Expression |
---|---|
neleq1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2203 |
. . 3
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2 | 1 | notbid 657 |
. 2
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3 | df-nel 2405 |
. 2
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4 | df-nel 2405 |
. 2
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5 | 2, 3, 4 | 3bitr4g 222 |
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-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-17 1507 ax-ial 1515 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-cleq 2133 df-clel 2136 df-nel 2405 |
This theorem is referenced by: neleq12d 2410 ruALT 4474 |
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