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Mirrors > Home > ILE Home > Th. List > findcard2d | Unicode version |
Description: Deduction version of findcard2 6791. 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 3122 |
. 2
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2 | findcard2d.a |
. . . 4
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3 | 2 | adantr 274 |
. . 3
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4 | sseq1 3125 |
. . . . . 6
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5 | 4 | anbi2d 460 |
. . . . 5
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6 | findcard2d.ch |
. . . . 5
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7 | 5, 6 | imbi12d 233 |
. . . 4
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8 | sseq1 3125 |
. . . . . 6
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9 | 8 | anbi2d 460 |
. . . . 5
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10 | findcard2d.th |
. . . . 5
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11 | 9, 10 | imbi12d 233 |
. . . 4
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12 | sseq1 3125 |
. . . . . 6
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13 | 12 | anbi2d 460 |
. . . . 5
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14 | findcard2d.ta |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | 13, 14 | imbi12d 233 |
. . . 4
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16 | sseq1 3125 |
. . . . . 6
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17 | 16 | anbi2d 460 |
. . . . 5
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18 | findcard2d.et |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
19 | 17, 18 | imbi12d 233 |
. . . 4
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20 | findcard2d.z |
. . . . 5
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21 | 20 | adantr 274 |
. . . 4
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22 | simprl 521 |
. . . . . . . 8
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23 | simprr 522 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
24 | 23 | unssad 3258 |
. . . . . . . 8
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25 | 22, 24 | jca 304 |
. . . . . . 7
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26 | id 19 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
27 | vsnid 3564 |
. . . . . . . . . . . 12
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28 | elun2 3249 |
. . . . . . . . . . . 12
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
29 | 27, 28 | mp1i 10 |
. . . . . . . . . . 11
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30 | 26, 29 | sseldd 3103 |
. . . . . . . . . 10
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31 | 30 | ad2antll 483 |
. . . . . . . . 9
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32 | simplr 520 |
. . . . . . . . 9
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33 | 31, 32 | eldifd 3086 |
. . . . . . . 8
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34 | findcard2d.i |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
35 | 22, 24, 33, 34 | syl12anc 1215 |
. . . . . . 7
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36 | 25, 35 | embantd 56 |
. . . . . 6
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37 | 36 | ex 114 |
. . . . 5
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38 | 37 | com23 78 |
. . . 4
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39 | 7, 11, 15, 19, 21, 38 | findcard2s 6792 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
40 | 3, 39 | mpcom 36 |
. 2
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41 | 1, 40 | mpan2 422 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-coll 4051 ax-sep 4054 ax-nul 4062 ax-pow 4106 ax-pr 4139 ax-un 4363 ax-setind 4460 ax-iinf 4510 |
This theorem depends on definitions: df-bi 116 df-dc 821 df-3or 964 df-3an 965 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ne 2310 df-ral 2422 df-rex 2423 df-reu 2424 df-rab 2426 df-v 2691 df-sbc 2914 df-csb 3008 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-nul 3369 df-if 3480 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-int 3780 df-iun 3823 df-br 3938 df-opab 3998 df-mpt 3999 df-tr 4035 df-id 4223 df-iord 4296 df-on 4298 df-suc 4301 df-iom 4513 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-res 4559 df-ima 4560 df-iota 5096 df-fun 5133 df-fn 5134 df-f 5135 df-f1 5136 df-fo 5137 df-f1o 5138 df-fv 5139 df-er 6437 df-en 6643 df-fin 6645 |
This theorem is referenced by: iunfidisj 6842 |
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