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Mirrors > Home > ILE Home > Th. List > nelne2 | Unicode version |
Description: Two classes are different if they don't belong to the same class. (Contributed by NM, 25-Jun-2012.) |
Ref | Expression |
---|---|
nelne2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1 2240 |
. . . 4
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2 | 1 | biimpcd 159 |
. . 3
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3 | 2 | necon3bd 2390 |
. 2
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4 | 3 | imp 124 |
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 614 ax-in2 615 ax-5 1447 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-4 1510 ax-17 1526 ax-ial 1534 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-cleq 2170 df-clel 2173 df-ne 2348 |
This theorem is referenced by: nelelne 2439 elnelne2 2452 zgt1rpn0n1 9679 |
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