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Mirrors > Home > MPE Home > Th. List > cardprclem | Structured version Unicode version |
Description: Lemma for cardprc 8264. (Contributed by Mario Carneiro, 22-Jan-2013.) (Revised by Mario Carneiro, 15-May-2015.) |
Ref | Expression |
---|---|
cardprclem.1 |
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Ref | Expression |
---|---|
cardprclem |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cardprclem.1 |
. . . . . . . . 9
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2 | 1 | eleq2i 2532 |
. . . . . . . 8
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3 | abid 2441 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | iscard 8259 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 2, 3, 4 | 3bitri 271 |
. . . . . . 7
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6 | 5 | simplbi 460 |
. . . . . 6
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7 | 6 | ssriv 3471 |
. . . . 5
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8 | ssonuni 6511 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 7, 8 | mpi 17 |
. . . 4
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10 | domrefg 7457 |
. . . . 5
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11 | 9, 10 | syl 16 |
. . . 4
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12 | elharval 7892 |
. . . 4
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13 | 9, 11, 12 | sylanbrc 664 |
. . 3
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14 | 7 | sseli 3463 |
. . . . . . . 8
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15 | domrefg 7457 |
. . . . . . . . . 10
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16 | 15 | ancli 551 |
. . . . . . . . 9
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17 | elharval 7892 |
. . . . . . . . 9
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18 | 16, 17 | sylibr 212 |
. . . . . . . 8
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19 | 14, 18 | syl 16 |
. . . . . . 7
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20 | harcard 8262 |
. . . . . . . 8
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21 | fvex 5812 |
. . . . . . . . 9
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22 | fveq2 5802 |
. . . . . . . . . 10
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23 | id 22 |
. . . . . . . . . 10
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24 | 22, 23 | eqeq12d 2476 |
. . . . . . . . 9
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25 | 21, 24, 1 | elab2 3216 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 20, 25 | mpbir 209 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | eleq2 2527 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
28 | eleq1 2526 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
29 | 27, 28 | anbi12d 710 |
. . . . . . . 8
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30 | 21, 29 | spcev 3170 |
. . . . . . 7
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31 | 19, 26, 30 | sylancl 662 |
. . . . . 6
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32 | eluni 4205 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
33 | 31, 32 | sylibr 212 |
. . . . 5
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34 | 33 | ssriv 3471 |
. . . 4
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35 | harcard 8262 |
. . . . 5
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36 | fvex 5812 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
37 | fveq2 5802 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
38 | id 22 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
39 | 37, 38 | eqeq12d 2476 |
. . . . . 6
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40 | 36, 39, 1 | elab2 3216 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
41 | 35, 40 | mpbir 209 |
. . . 4
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42 | 34, 41 | sselii 3464 |
. . 3
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43 | 13, 42 | jctir 538 |
. 2
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44 | eloni 4840 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
45 | ordn2lp 4850 |
. . 3
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46 | 9, 44, 45 | 3syl 20 |
. 2
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47 | 43, 46 | pm2.65i 173 |
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 4514 ax-sep 4524 ax-nul 4532 ax-pow 4581 ax-pr 4642 ax-un 6485 |
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-rmo 2807 df-rab 2808 df-v 3080 df-sbc 3295 df-csb 3399 df-dif 3442 df-un 3444 df-in 3446 df-ss 3453 df-pss 3455 df-nul 3749 df-if 3903 df-pw 3973 df-sn 3989 df-pr 3991 df-tp 3993 df-op 3995 df-uni 4203 df-int 4240 df-iun 4284 df-br 4404 df-opab 4462 df-mpt 4463 df-tr 4497 df-eprel 4743 df-id 4747 df-po 4752 df-so 4753 df-fr 4790 df-se 4791 df-we 4792 df-ord 4833 df-on 4834 df-lim 4835 df-suc 4836 df-xp 4957 df-rel 4958 df-cnv 4959 df-co 4960 df-dm 4961 df-rn 4962 df-res 4963 df-ima 4964 df-iota 5492 df-fun 5531 df-fn 5532 df-f 5533 df-f1 5534 df-fo 5535 df-f1o 5536 df-fv 5537 df-isom 5538 df-riota 6164 df-recs 6945 df-er 7214 df-en 7424 df-dom 7425 df-sdom 7426 df-oi 7838 df-har 7887 df-card 8223 |
This theorem is referenced by: cardprc 8264 |
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