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Mirrors > Home > MPE Home > Th. List > r1pw | Structured version Unicode version |
Description: A stronger property of
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Ref | Expression |
---|---|
r1pw |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rankpwi 8142 |
. . . . . 6
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2 | 1 | eleq1d 2523 |
. . . . 5
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3 | eloni 4838 |
. . . . . . 7
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4 | ordsucelsuc 6544 |
. . . . . . 7
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5 | 3, 4 | syl 16 |
. . . . . 6
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6 | 5 | bicomd 201 |
. . . . 5
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7 | 2, 6 | sylan9bb 699 |
. . . 4
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8 | pwwf 8126 |
. . . . . 6
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9 | 8 | biimpi 194 |
. . . . 5
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10 | suceloni 6535 |
. . . . . 6
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11 | r1fnon 8086 |
. . . . . . 7
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12 | fndm 5619 |
. . . . . . 7
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13 | 11, 12 | ax-mp 5 |
. . . . . 6
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14 | 10, 13 | syl6eleqr 2553 |
. . . . 5
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15 | rankr1ag 8121 |
. . . . 5
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16 | 9, 14, 15 | syl2an 477 |
. . . 4
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17 | 13 | eleq2i 2532 |
. . . . 5
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18 | rankr1ag 8121 |
. . . . 5
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19 | 17, 18 | sylan2br 476 |
. . . 4
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20 | 7, 16, 19 | 3bitr4rd 286 |
. . 3
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21 | 20 | ex 434 |
. 2
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22 | r1elwf 8115 |
. . . 4
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23 | r1elwf 8115 |
. . . . . 6
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24 | r1elssi 8124 |
. . . . . 6
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25 | 23, 24 | syl 16 |
. . . . 5
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26 | ssid 3484 |
. . . . . 6
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27 | elex 3087 |
. . . . . . . 8
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28 | pwexb 6498 |
. . . . . . . 8
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29 | 27, 28 | sylibr 212 |
. . . . . . 7
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30 | elpwg 3977 |
. . . . . . 7
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31 | 29, 30 | syl 16 |
. . . . . 6
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32 | 26, 31 | mpbiri 233 |
. . . . 5
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33 | 25, 32 | sseldd 3466 |
. . . 4
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34 | 22, 33 | pm5.21ni 352 |
. . 3
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35 | 34 | a1d 25 |
. 2
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36 | 21, 35 | pm2.61i 164 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 ax-rep 4512 ax-sep 4522 ax-nul 4530 ax-pow 4579 ax-pr 4640 ax-un 6483 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 966 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2266 df-mo 2267 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ne 2650 df-ral 2804 df-rex 2805 df-reu 2806 df-rab 2808 df-v 3080 df-sbc 3295 df-csb 3397 df-dif 3440 df-un 3442 df-in 3444 df-ss 3451 df-pss 3453 df-nul 3747 df-if 3901 df-pw 3971 df-sn 3987 df-pr 3989 df-tp 3991 df-op 3993 df-uni 4201 df-int 4238 df-iun 4282 df-br 4402 df-opab 4460 df-mpt 4461 df-tr 4495 df-eprel 4741 df-id 4745 df-po 4750 df-so 4751 df-fr 4788 df-we 4790 df-ord 4831 df-on 4832 df-lim 4833 df-suc 4834 df-xp 4955 df-rel 4956 df-cnv 4957 df-co 4958 df-dm 4959 df-rn 4960 df-res 4961 df-ima 4962 df-iota 5490 df-fun 5529 df-fn 5530 df-f 5531 df-f1 5532 df-fo 5533 df-f1o 5534 df-fv 5535 df-om 6588 df-recs 6943 df-rdg 6977 df-r1 8083 df-rank 8084 |
This theorem is referenced by: inatsk 9057 |
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