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Mirrors > Home > ILE Home > Th. List > Mathboxes > bj-charfundcALT | Unicode version |
Description: Alternate proof of bj-charfundc 15370. It was expected to be much shorter since it uses bj-charfun 15369 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 15369 |
. 2
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3 | difin 3397 |
. . . . . . . . . . . 12
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4 | 3 | eqcomi 2197 |
. . . . . . . . . . 11
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5 | 4 | a1i 9 |
. . . . . . . . . 10
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6 | 5 | uneq2d 3314 |
. . . . . . . . 9
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7 | inss1 3380 |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 7 | a1i 9 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | bj-charfundc.dc |
. . . . . . . . . . 11
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | elin 3343 |
. . . . . . . . . . . . . 14
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
11 | 10 | baibr 921 |
. . . . . . . . . . . . 13
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12 | 11 | dcbid 839 |
. . . . . . . . . . . 12
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13 | 12 | ralbiia 2508 |
. . . . . . . . . . 11
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14 | 9, 13 | sylib 122 |
. . . . . . . . . 10
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15 | undifdcss 6981 |
. . . . . . . . . 10
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16 | 8, 14, 15 | sylanbrc 417 |
. . . . . . . . 9
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17 | 6, 16 | eqtr4d 2229 |
. . . . . . . 8
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18 | 17 | reseq2d 4943 |
. . . . . . 7
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19 | ssidd 3201 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
20 | 19 | resmptd 4994 |
. . . . . . . 8
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21 | 1 | reseq1d 4942 |
. . . . . . . 8
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22 | 20, 21, 1 | 3eqtr4d 2236 |
. . . . . . 7
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23 | 18, 22 | eqtrd 2226 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 23, 17 | feq12d 5394 |
. . . . 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 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 2166 ax-14 2167 ax-ext 2175 ax-sep 4148 ax-nul 4156 ax-pow 4204 ax-pr 4239 ax-un 4465 |
This theorem depends on definitions: df-bi 117 df-dc 836 df-3an 982 df-tru 1367 df-fal 1370 df-nf 1472 df-sb 1774 df-eu 2045 df-mo 2046 df-clab 2180 df-cleq 2186 df-clel 2189 df-nfc 2325 df-ral 2477 df-rex 2478 df-rab 2481 df-v 2762 df-sbc 2987 df-csb 3082 df-dif 3156 df-un 3158 df-in 3160 df-ss 3167 df-nul 3448 df-if 3559 df-pw 3604 df-sn 3625 df-pr 3626 df-op 3628 df-uni 3837 df-br 4031 df-opab 4092 df-mpt 4093 df-tr 4129 df-id 4325 df-iord 4398 df-on 4400 df-suc 4403 df-xp 4666 df-rel 4667 df-cnv 4668 df-co 4669 df-dm 4670 df-rn 4671 df-res 4672 df-ima 4673 df-iota 5216 df-fun 5257 df-fn 5258 df-f 5259 df-fv 5263 df-1o 6471 df-2o 6472 |
This theorem is referenced by: (None) |
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