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Mirrors > Home > ILE Home > Th. List > findcard2d | Unicode version |
Description: Deduction version of findcard2 6605. If you also need ![]() ![]() ![]() |
Ref | Expression |
---|---|
findcard2d.ch |
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findcard2d.th |
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findcard2d.ta |
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findcard2d.et |
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findcard2d.z |
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findcard2d.i |
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findcard2d.a |
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Ref | Expression |
---|---|
findcard2d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssid 3044 |
. 2
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2 | findcard2d.a |
. . . 4
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3 | 2 | adantr 270 |
. . 3
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4 | sseq1 3047 |
. . . . . 6
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5 | 4 | anbi2d 452 |
. . . . 5
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6 | findcard2d.ch |
. . . . 5
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7 | 5, 6 | imbi12d 232 |
. . . 4
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8 | sseq1 3047 |
. . . . . 6
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9 | 8 | anbi2d 452 |
. . . . 5
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10 | findcard2d.th |
. . . . 5
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11 | 9, 10 | imbi12d 232 |
. . . 4
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12 | sseq1 3047 |
. . . . . 6
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13 | 12 | anbi2d 452 |
. . . . 5
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14 | findcard2d.ta |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | 13, 14 | imbi12d 232 |
. . . 4
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16 | sseq1 3047 |
. . . . . 6
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17 | 16 | anbi2d 452 |
. . . . 5
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18 | findcard2d.et |
. . . . 5
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19 | 17, 18 | imbi12d 232 |
. . . 4
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20 | findcard2d.z |
. . . . 5
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21 | 20 | adantr 270 |
. . . 4
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22 | simprl 498 |
. . . . . . . 8
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23 | simprr 499 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
24 | 23 | unssad 3177 |
. . . . . . . 8
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25 | 22, 24 | jca 300 |
. . . . . . 7
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26 | id 19 |
. . . . . . . . . . 11
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27 | vsnid 3476 |
. . . . . . . . . . . 12
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28 | elun2 3168 |
. . . . . . . . . . . 12
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29 | 27, 28 | mp1i 10 |
. . . . . . . . . . 11
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30 | 26, 29 | sseldd 3026 |
. . . . . . . . . 10
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31 | 30 | ad2antll 475 |
. . . . . . . . 9
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32 | simplr 497 |
. . . . . . . . 9
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33 | 31, 32 | eldifd 3009 |
. . . . . . . 8
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34 | findcard2d.i |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
35 | 22, 24, 33, 34 | syl12anc 1172 |
. . . . . . 7
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36 | 25, 35 | embantd 55 |
. . . . . 6
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37 | 36 | ex 113 |
. . . . 5
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38 | 37 | com23 77 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
39 | 7, 11, 15, 19, 21, 38 | findcard2s 6606 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
40 | 3, 39 | mpcom 36 |
. 2
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41 | 1, 40 | mpan2 416 |
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-13 1449 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-coll 3954 ax-sep 3957 ax-nul 3965 ax-pow 4009 ax-pr 4036 ax-un 4260 ax-setind 4353 ax-iinf 4403 |
This theorem depends on definitions: df-bi 115 df-dc 781 df-3or 925 df-3an 926 df-tru 1292 df-fal 1295 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ne 2256 df-ral 2364 df-rex 2365 df-reu 2366 df-rab 2368 df-v 2621 df-sbc 2841 df-csb 2934 df-dif 3001 df-un 3003 df-in 3005 df-ss 3012 df-nul 3287 df-if 3394 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-int 3689 df-iun 3732 df-br 3846 df-opab 3900 df-mpt 3901 df-tr 3937 df-id 4120 df-iord 4193 df-on 4195 df-suc 4198 df-iom 4406 df-xp 4444 df-rel 4445 df-cnv 4446 df-co 4447 df-dm 4448 df-rn 4449 df-res 4450 df-ima 4451 df-iota 4980 df-fun 5017 df-fn 5018 df-f 5019 df-f1 5020 df-fo 5021 df-f1o 5022 df-fv 5023 df-er 6292 df-en 6458 df-fin 6460 |
This theorem is referenced by: iunfidisj 6655 |
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