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Mirrors > Home > ILE Home > Th. List > snon0 | Unicode version |
Description: An ordinal which is a
singleton is ![]() ![]() ![]() |
Ref | Expression |
---|---|
snon0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elirr 4538 |
. . 3
![]() ![]() ![]() ![]() ![]() | |
2 | snidg 3621 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 2 | adantr 276 |
. . . . . 6
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4 | ontr1 4387 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 4 | adantl 277 |
. . . . . 6
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6 | 3, 5 | mpan2d 428 |
. . . . 5
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7 | elsni 3610 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 6, 7 | syl6 33 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | eleq1 2240 |
. . . . 5
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10 | 9 | biimpcd 159 |
. . . 4
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11 | 8, 10 | sylcom 28 |
. . 3
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12 | 1, 11 | mtoi 664 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | 12 | eq0rdv 3467 |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-setind 4534 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-ral 2460 df-rex 2461 df-v 2739 df-dif 3131 df-in 3135 df-ss 3142 df-nul 3423 df-sn 3598 df-uni 3809 df-tr 4100 df-iord 4364 df-on 4366 |
This theorem is referenced by: (None) |
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