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Mirrors > Home > ILE Home > Th. List > ordtriexmidlem2 | Unicode version |
Description: Lemma for decidability
and ordinals. The set ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
ordtriexmidlem2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | noel 3290 |
. . 3
![]() ![]() ![]() ![]() ![]() | |
2 | eleq2 2151 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 1, 2 | mtbiri 635 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | 0ex 3966 |
. . . 4
![]() ![]() ![]() ![]() | |
5 | 4 | snid 3475 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() |
6 | biidd 170 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | 6 | elrab3 2772 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
8 | 5, 7 | ax-mp 7 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | 3, 8 | sylnib 636 |
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 ax-nul 3965 |
This theorem depends on definitions: df-bi 115 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-rab 2368 df-v 2621 df-dif 3001 df-nul 3287 df-sn 3452 |
This theorem is referenced by: ordtriexmid 4338 ordtri2orexmid 4339 ontr2exmid 4341 onsucsssucexmid 4343 ordsoexmid 4378 0elsucexmid 4381 ordpwsucexmid 4386 |
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