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Mirrors > Home > ILE Home > Th. List > findcard2d | Unicode version |
Description: Deduction version of findcard2 6917. 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 3190 |
. 2
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2 | findcard2d.a |
. . . 4
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3 | 2 | adantr 276 |
. . 3
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4 | sseq1 3193 |
. . . . . 6
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5 | 4 | anbi2d 464 |
. . . . 5
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6 | findcard2d.ch |
. . . . 5
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7 | 5, 6 | imbi12d 234 |
. . . 4
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8 | sseq1 3193 |
. . . . . 6
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9 | 8 | anbi2d 464 |
. . . . 5
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10 | findcard2d.th |
. . . . 5
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11 | 9, 10 | imbi12d 234 |
. . . 4
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12 | sseq1 3193 |
. . . . . 6
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13 | 12 | anbi2d 464 |
. . . . 5
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14 | findcard2d.ta |
. . . . 5
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15 | 13, 14 | imbi12d 234 |
. . . 4
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16 | sseq1 3193 |
. . . . . 6
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17 | 16 | anbi2d 464 |
. . . . 5
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18 | findcard2d.et |
. . . . 5
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19 | 17, 18 | imbi12d 234 |
. . . 4
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20 | findcard2d.z |
. . . . 5
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21 | 20 | adantr 276 |
. . . 4
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22 | simprl 529 |
. . . . . . . 8
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23 | simprr 531 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
24 | 23 | unssad 3327 |
. . . . . . . 8
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25 | 22, 24 | jca 306 |
. . . . . . 7
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26 | id 19 |
. . . . . . . . . . 11
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27 | vsnid 3639 |
. . . . . . . . . . . 12
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28 | elun2 3318 |
. . . . . . . . . . . 12
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29 | 27, 28 | mp1i 10 |
. . . . . . . . . . 11
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30 | 26, 29 | sseldd 3171 |
. . . . . . . . . 10
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31 | 30 | ad2antll 491 |
. . . . . . . . 9
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32 | simplr 528 |
. . . . . . . . 9
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33 | 31, 32 | eldifd 3154 |
. . . . . . . 8
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34 | findcard2d.i |
. . . . . . . 8
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35 | 22, 24, 33, 34 | syl12anc 1247 |
. . . . . . 7
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36 | 25, 35 | embantd 56 |
. . . . . 6
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37 | 36 | ex 115 |
. . . . 5
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38 | 37 | com23 78 |
. . . 4
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39 | 7, 11, 15, 19, 21, 38 | findcard2s 6918 |
. . 3
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40 | 3, 39 | mpcom 36 |
. 2
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41 | 1, 40 | mpan2 425 |
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 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-coll 4133 ax-sep 4136 ax-nul 4144 ax-pow 4192 ax-pr 4227 ax-un 4451 ax-setind 4554 ax-iinf 4605 |
This theorem depends on definitions: df-bi 117 df-dc 836 df-3or 981 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ne 2361 df-ral 2473 df-rex 2474 df-reu 2475 df-rab 2477 df-v 2754 df-sbc 2978 df-csb 3073 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-nul 3438 df-if 3550 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-int 3860 df-iun 3903 df-br 4019 df-opab 4080 df-mpt 4081 df-tr 4117 df-id 4311 df-iord 4384 df-on 4386 df-suc 4389 df-iom 4608 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-rn 4655 df-res 4656 df-ima 4657 df-iota 5196 df-fun 5237 df-fn 5238 df-f 5239 df-f1 5240 df-fo 5241 df-f1o 5242 df-fv 5243 df-er 6559 df-en 6767 df-fin 6769 |
This theorem is referenced by: iunfidisj 6975 |
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