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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 4385 |
. . 3
![]() ![]() ![]() ![]() ![]() | |
2 | snidg 3493 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 2 | adantr 271 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | ontr1 4240 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 4 | adantl 272 |
. . . . . 6
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6 | 3, 5 | mpan2d 420 |
. . . . 5
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7 | elsni 3484 |
. . . . 5
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8 | 6, 7 | syl6 33 |
. . . 4
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9 | eleq1 2157 |
. . . . 5
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10 | 9 | biimpcd 158 |
. . . 4
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11 | 8, 10 | sylcom 28 |
. . 3
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12 | 1, 11 | mtoi 628 |
. 2
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13 | 12 | eq0rdv 3346 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 582 ax-in2 583 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-setind 4381 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-nf 1402 df-sb 1700 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ne 2263 df-ral 2375 df-rex 2376 df-v 2635 df-dif 3015 df-in 3019 df-ss 3026 df-nul 3303 df-sn 3472 df-uni 3676 df-tr 3959 df-iord 4217 df-on 4219 |
This theorem is referenced by: (None) |
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