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Mirrors > Home > ILE Home > Th. List > nbrne2 | Unicode version |
Description: Two classes are different if they don't have the same relationship to a third class. (Contributed by NM, 3-Jun-2012.) |
Ref | Expression |
---|---|
nbrne2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq1 3848 |
. . . 4
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2 | 1 | biimpcd 157 |
. . 3
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3 | 2 | necon3bd 2298 |
. 2
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4 | 3 | imp 122 |
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 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ne 2256 df-v 2621 df-un 3003 df-sn 3452 df-pr 3453 df-op 3455 df-br 3846 |
This theorem is referenced by: (None) |
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