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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-charfundcALT | Unicode version |
Description: Alternate proof of bj-charfundc 14599. It was expected to be much shorter since it uses bj-charfun 14598 for the main part of the proof and the rest is basic computations, but these turn out to be lengthy, maybe because of the limited library of available lemmas. (Contributed by BJ, 15-Aug-2024.) (Proof modification is discouraged.) (New usage is discouraged.) |
Ref | Expression |
---|---|
bj-charfundc.1 |
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bj-charfundc.dc |
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Ref | Expression |
---|---|
bj-charfundcALT |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-charfundc.1 |
. . 3
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2 | 1 | bj-charfun 14598 |
. 2
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3 | difin 3374 |
. . . . . . . . . . . 12
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4 | 3 | eqcomi 2181 |
. . . . . . . . . . 11
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5 | 4 | a1i 9 |
. . . . . . . . . 10
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6 | 5 | uneq2d 3291 |
. . . . . . . . 9
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7 | inss1 3357 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 7 | a1i 9 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | bj-charfundc.dc |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | elin 3320 |
. . . . . . . . . . . . . 14
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
11 | 10 | baibr 920 |
. . . . . . . . . . . . 13
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12 | 11 | dcbid 838 |
. . . . . . . . . . . 12
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13 | 12 | ralbiia 2491 |
. . . . . . . . . . 11
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14 | 9, 13 | sylib 122 |
. . . . . . . . . 10
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15 | undifdcss 6924 |
. . . . . . . . . 10
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16 | 8, 14, 15 | sylanbrc 417 |
. . . . . . . . 9
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17 | 6, 16 | eqtr4d 2213 |
. . . . . . . 8
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18 | 17 | reseq2d 4909 |
. . . . . . 7
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19 | ssidd 3178 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
20 | 19 | resmptd 4960 |
. . . . . . . 8
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21 | 1 | reseq1d 4908 |
. . . . . . . 8
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22 | 20, 21, 1 | 3eqtr4d 2220 |
. . . . . . 7
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23 | 18, 22 | eqtrd 2210 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 23, 17 | feq12d 5357 |
. . . . 5
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25 | 24 | biimpd 144 |
. . . 4
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26 | 25 | adantld 278 |
. . 3
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27 | 26 | anim1d 336 |
. 2
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28 | 2, 27 | mpd 13 |
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 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4123 ax-nul 4131 ax-pow 4176 ax-pr 4211 ax-un 4435 |
This theorem depends on definitions: df-bi 117 df-dc 835 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2741 df-sbc 2965 df-csb 3060 df-dif 3133 df-un 3135 df-in 3137 df-ss 3144 df-nul 3425 df-if 3537 df-pw 3579 df-sn 3600 df-pr 3601 df-op 3603 df-uni 3812 df-br 4006 df-opab 4067 df-mpt 4068 df-tr 4104 df-id 4295 df-iord 4368 df-on 4370 df-suc 4373 df-xp 4634 df-rel 4635 df-cnv 4636 df-co 4637 df-dm 4638 df-rn 4639 df-res 4640 df-ima 4641 df-iota 5180 df-fun 5220 df-fn 5221 df-f 5222 df-fv 5226 df-1o 6419 df-2o 6420 |
This theorem is referenced by: (None) |
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