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Mirrors > Home > ILE Home > Th. List > frec2uzlt2d | Unicode version |
Description: The mapping ![]() |
Ref | Expression |
---|---|
frec2uz.1 |
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frec2uz.2 |
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frec2uzzd.a |
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frec2uzltd.b |
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Ref | Expression |
---|---|
frec2uzlt2d |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frec2uz.1 |
. . 3
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2 | frec2uz.2 |
. . 3
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3 | frec2uzzd.a |
. . 3
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4 | frec2uzltd.b |
. . 3
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5 | 1, 2, 3, 4 | frec2uzltd 10421 |
. 2
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6 | nntri3or 6512 |
. . . 4
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7 | 3, 4, 6 | syl2anc 411 |
. . 3
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8 | ax-1 6 |
. . . . 5
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9 | 8 | a1i 9 |
. . . 4
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10 | fveq2 5530 |
. . . . . . . . . 10
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11 | 10 | adantl 277 |
. . . . . . . . 9
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12 | 11 | breq2d 4030 |
. . . . . . . 8
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13 | 12 | biimpar 297 |
. . . . . . 7
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14 | 1, 2, 3 | frec2uzzd 10418 |
. . . . . . . . . . 11
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15 | 14 | adantr 276 |
. . . . . . . . . 10
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16 | 15 | adantr 276 |
. . . . . . . . 9
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17 | 16 | zred 9393 |
. . . . . . . 8
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18 | 17 | ltnrd 8087 |
. . . . . . 7
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19 | 13, 18 | pm2.21dd 621 |
. . . . . 6
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20 | 19 | ex 115 |
. . . . 5
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21 | 20 | ex 115 |
. . . 4
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22 | 1, 2, 4 | frec2uzzd 10418 |
. . . . . . . . 9
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23 | 22 | adantr 276 |
. . . . . . . 8
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24 | 23 | zred 9393 |
. . . . . . 7
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25 | 14 | adantr 276 |
. . . . . . . 8
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26 | 25 | zred 9393 |
. . . . . . 7
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27 | 1, 2, 4, 3 | frec2uzltd 10421 |
. . . . . . . 8
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28 | 27 | imp 124 |
. . . . . . 7
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29 | 24, 26, 28 | ltnsymd 8095 |
. . . . . 6
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30 | 29 | pm2.21d 620 |
. . . . 5
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31 | 30 | ex 115 |
. . . 4
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32 | 9, 21, 31 | 3jaod 1315 |
. . 3
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33 | 7, 32 | mpd 13 |
. 2
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34 | 5, 33 | impbid 129 |
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 4189 ax-pr 4224 ax-un 4448 ax-setind 4551 ax-iinf 4602 ax-cnex 7920 ax-resscn 7921 ax-1cn 7922 ax-1re 7923 ax-icn 7924 ax-addcl 7925 ax-addrcl 7926 ax-mulcl 7927 ax-addcom 7929 ax-addass 7931 ax-distr 7933 ax-i2m1 7934 ax-0lt1 7935 ax-0id 7937 ax-rnegex 7938 ax-cnre 7940 ax-pre-ltirr 7941 ax-pre-ltwlin 7942 ax-pre-lttrn 7943 ax-pre-ltadd 7945 |
This theorem depends on definitions: df-bi 117 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-nel 2456 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-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 4308 df-iord 4381 df-on 4383 df-ilim 4384 df-suc 4386 df-iom 4605 df-xp 4647 df-rel 4648 df-cnv 4649 df-co 4650 df-dm 4651 df-rn 4652 df-res 4653 df-ima 4654 df-iota 5193 df-fun 5233 df-fn 5234 df-f 5235 df-f1 5236 df-fo 5237 df-f1o 5238 df-fv 5239 df-riota 5847 df-ov 5894 df-oprab 5895 df-mpo 5896 df-recs 6324 df-frec 6410 df-pnf 8012 df-mnf 8013 df-xr 8014 df-ltxr 8015 df-le 8016 df-sub 8148 df-neg 8149 df-inn 8938 df-n0 9195 df-z 9272 df-uz 9547 |
This theorem is referenced by: frec2uzisod 10425 frec2uzled 10447 |
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