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Mirrors > Home > ILE Home > Th. List > fmptcof | Unicode version |
Description: Version of fmptco 5703 where ![]() ![]() |
Ref | Expression |
---|---|
fmptcof.1 |
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fmptcof.2 |
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fmptcof.3 |
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fmptcof.4 |
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Ref | Expression |
---|---|
fmptcof |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fmptcof.1 |
. . . . 5
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2 | nfcsb1v 3105 |
. . . . . . 7
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3 | 2 | nfel1 2343 |
. . . . . 6
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4 | csbeq1a 3081 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 4 | eleq1d 2258 |
. . . . . 6
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6 | 3, 5 | rspc 2850 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | 1, 6 | mpan9 281 |
. . . 4
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8 | fmptcof.2 |
. . . . 5
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9 | nfcv 2332 |
. . . . . 6
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10 | 9, 2, 4 | cbvmpt 4113 |
. . . . 5
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11 | 8, 10 | eqtrdi 2238 |
. . . 4
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12 | fmptcof.3 |
. . . . 5
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13 | nfcv 2332 |
. . . . . 6
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14 | nfcsb1v 3105 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | csbeq1a 3081 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
16 | 13, 14, 15 | cbvmpt 4113 |
. . . . 5
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17 | 12, 16 | eqtrdi 2238 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | csbeq1 3075 |
. . . 4
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19 | 7, 11, 17, 18 | fmptco 5703 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | nfcv 2332 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | nfcv 2332 |
. . . . 5
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22 | 2, 21 | nfcsb 3109 |
. . . 4
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23 | 4 | csbeq1d 3079 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 20, 22, 23 | cbvmpt 4113 |
. . 3
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25 | 19, 24 | eqtr4di 2240 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | eqid 2189 |
. . . 4
![]() ![]() ![]() ![]() | |
27 | nfcvd 2333 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
28 | fmptcof.4 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
29 | 27, 28 | csbiegf 3115 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
30 | 29 | ralimi 2553 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
31 | mpteq12 4101 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
32 | 26, 30, 31 | sylancr 414 |
. . 3
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33 | 1, 32 | syl 14 |
. 2
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34 | 25, 33 | eqtrd 2222 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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-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-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 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-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-sbc 2978 df-csb 3073 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-br 4019 df-opab 4080 df-mpt 4081 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-rn 4655 df-res 4656 df-ima 4657 df-iota 5196 df-fun 5237 df-fn 5238 df-f 5239 df-fv 5243 |
This theorem is referenced by: fmptcos 5705 cncfmpt1f 14544 sincn 14650 coscn 14651 |
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