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Mirrors > Home > ILE Home > Th. List > recvguniqlem | Unicode version |
Description: Lemma for recvguniq 11021. Some of the rearrangements of the expressions. (Contributed by Jim Kingdon, 8-Aug-2021.) |
Ref | Expression |
---|---|
recvguniqlem.f |
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recvguniqlem.a |
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recvguniqlem.b |
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recvguniqlem.k |
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recvguniqlem.lt1 |
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recvguniqlem.lt2 |
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Ref | Expression |
---|---|
recvguniqlem |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | recvguniqlem.a |
. . 3
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2 | recvguniqlem.f |
. . . . 5
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3 | recvguniqlem.k |
. . . . 5
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4 | 2, 3 | ffvelcdmd 5667 |
. . . 4
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5 | recvguniqlem.b |
. . . . . 6
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6 | 1, 5 | resubcld 8355 |
. . . . 5
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7 | 6 | rehalfcld 9182 |
. . . 4
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8 | 4, 7 | readdcld 8004 |
. . 3
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9 | recvguniqlem.lt1 |
. . 3
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10 | 5, 7 | readdcld 8004 |
. . . . 5
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11 | recvguniqlem.lt2 |
. . . . 5
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12 | 4, 10, 7, 11 | ltadd1dd 8530 |
. . . 4
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13 | 5 | recnd 8003 |
. . . . . 6
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14 | 7 | recnd 8003 |
. . . . . 6
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15 | 13, 14, 14 | addassd 7997 |
. . . . 5
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16 | 6 | recnd 8003 |
. . . . . . 7
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17 | 16 | 2halvesd 9181 |
. . . . . 6
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18 | 17 | oveq2d 5906 |
. . . . 5
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19 | 1 | recnd 8003 |
. . . . . 6
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20 | 13, 19 | pncan3d 8288 |
. . . . 5
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21 | 15, 18, 20 | 3eqtrd 2225 |
. . . 4
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22 | 12, 21 | breqtrd 4043 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 1, 8, 1, 9, 22 | lttrd 8100 |
. 2
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24 | 1 | ltnrd 8086 |
. 2
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25 | 23, 24 | pm2.21fal 1383 |
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 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-bndl 1519 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 ax-13 2161 ax-14 2162 ax-ext 2170 ax-sep 4135 ax-pow 4188 ax-pr 4223 ax-un 4447 ax-setind 4550 ax-cnex 7919 ax-resscn 7920 ax-1cn 7921 ax-1re 7922 ax-icn 7923 ax-addcl 7924 ax-addrcl 7925 ax-mulcl 7926 ax-mulrcl 7927 ax-addcom 7928 ax-mulcom 7929 ax-addass 7930 ax-mulass 7931 ax-distr 7932 ax-i2m1 7933 ax-0lt1 7934 ax-1rid 7935 ax-0id 7936 ax-rnegex 7937 ax-precex 7938 ax-cnre 7939 ax-pre-ltirr 7940 ax-pre-ltwlin 7941 ax-pre-lttrn 7942 ax-pre-apti 7943 ax-pre-ltadd 7944 ax-pre-mulgt0 7945 ax-pre-mulext 7946 |
This theorem depends on definitions: df-bi 117 df-3an 981 df-tru 1366 df-fal 1369 df-nf 1471 df-sb 1773 df-eu 2040 df-mo 2041 df-clab 2175 df-cleq 2181 df-clel 2184 df-nfc 2320 df-ne 2360 df-nel 2455 df-ral 2472 df-rex 2473 df-reu 2474 df-rmo 2475 df-rab 2476 df-v 2753 df-sbc 2977 df-dif 3145 df-un 3147 df-in 3149 df-ss 3156 df-pw 3591 df-sn 3612 df-pr 3613 df-op 3615 df-uni 3824 df-br 4018 df-opab 4079 df-id 4307 df-po 4310 df-iso 4311 df-xp 4646 df-rel 4647 df-cnv 4648 df-co 4649 df-dm 4650 df-rn 4651 df-iota 5192 df-fun 5232 df-fn 5233 df-f 5234 df-fv 5238 df-riota 5846 df-ov 5893 df-oprab 5894 df-mpo 5895 df-pnf 8011 df-mnf 8012 df-xr 8013 df-ltxr 8014 df-le 8015 df-sub 8147 df-neg 8148 df-reap 8549 df-ap 8556 df-div 8647 df-2 8995 |
This theorem is referenced by: recvguniq 11021 |
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