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Mirrors > Home > MPE Home > Th. List > findcard2s | Structured version Visualization version Unicode version |
Description: Variation of findcard2 8200 requiring that the element added in the induction step not be a member of the original set. (Contributed by Paul Chapman, 30-Nov-2012.) |
Ref | Expression |
---|---|
findcard2s.1 | |
findcard2s.2 | |
findcard2s.3 | |
findcard2s.4 | |
findcard2s.5 | |
findcard2s.6 |
Ref | Expression |
---|---|
findcard2s |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | findcard2s.1 | . 2 | |
2 | findcard2s.2 | . 2 | |
3 | findcard2s.3 | . 2 | |
4 | findcard2s.4 | . 2 | |
5 | findcard2s.5 | . 2 | |
6 | findcard2s.6 | . . . 4 | |
7 | 6 | ex 450 | . . 3 |
8 | uncom 3757 | . . . . . . 7 | |
9 | snssi 4339 | . . . . . . . 8 | |
10 | ssequn1 3783 | . . . . . . . 8 | |
11 | 9, 10 | sylib 208 | . . . . . . 7 |
12 | 8, 11 | syl5reqr 2671 | . . . . . 6 |
13 | vex 3203 | . . . . . . 7 | |
14 | 13 | eqvinc 3330 | . . . . . 6 |
15 | 12, 14 | sylib 208 | . . . . 5 |
16 | 2 | bicomd 213 | . . . . . . 7 |
17 | 16, 3 | sylan9bb 736 | . . . . . 6 |
18 | 17 | exlimiv 1858 | . . . . 5 |
19 | 15, 18 | syl 17 | . . . 4 |
20 | 19 | biimpd 219 | . . 3 |
21 | 7, 20 | pm2.61d2 172 | . 2 |
22 | 1, 2, 3, 4, 5, 21 | findcard2 8200 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 196 wa 384 wceq 1483 wex 1704 wcel 1990 cun 3572 wss 3574 c0 3915 csn 4177 cfn 7955 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3or 1038 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-sbc 3436 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-pss 3590 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-tp 4182 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-tr 4753 df-id 5024 df-eprel 5029 df-po 5035 df-so 5036 df-fr 5073 df-we 5075 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-ord 5726 df-on 5727 df-lim 5728 df-suc 5729 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-om 7066 df-1o 7560 df-er 7742 df-en 7956 df-fin 7959 |
This theorem is referenced by: findcard2d 8202 ac6sfi 8204 domunfican 8233 fodomfi 8239 hashxplem 13220 hashmap 13222 hashbc 13237 hashf1lem2 13240 hashf1 13241 fsum2d 14502 fsumabs 14533 fsumrlim 14543 fsumo1 14544 fsumiun 14553 incexclem 14568 fprod2d 14711 coprmprod 15375 coprmproddvds 15377 gsum2dlem2 18370 ablfac1eulem 18471 mplcoe1 19465 mplcoe5 19468 coe1fzgsumd 19672 evl1gsumd 19721 mdetunilem9 20426 ptcmpfi 21616 tmdgsum 21899 fsumcn 22673 ovolfiniun 23269 volfiniun 23315 itgfsum 23593 dvmptfsum 23738 jensen 24715 gsumle 29779 gsumvsca1 29782 gsumvsca2 29783 finixpnum 33394 matunitlindflem1 33405 pwslnm 37664 fnchoice 39188 dvmptfprod 40160 |
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