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Mirrors > Home > ILE Home > Th. List > fmptcof | Unicode version |
Description: Version of fmptco 5478 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 2964 |
. . . . . . 7
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3 | 2 | nfel1 2240 |
. . . . . 6
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4 | csbeq1a 2942 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 4 | eleq1d 2157 |
. . . . . 6
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6 | 3, 5 | rspc 2717 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | 1, 6 | mpan9 276 |
. . . 4
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8 | fmptcof.2 |
. . . . 5
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9 | nfcv 2229 |
. . . . . 6
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10 | 9, 2, 4 | cbvmpt 3939 |
. . . . 5
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11 | 8, 10 | syl6eq 2137 |
. . . 4
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12 | fmptcof.3 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
13 | nfcv 2229 |
. . . . . 6
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14 | nfcsb1v 2964 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | csbeq1a 2942 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
16 | 13, 14, 15 | cbvmpt 3939 |
. . . . 5
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17 | 12, 16 | syl6eq 2137 |
. . . 4
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18 | csbeq1 2937 |
. . . 4
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19 | 7, 11, 17, 18 | fmptco 5478 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | nfcv 2229 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | nfcv 2229 |
. . . . 5
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22 | 2, 21 | nfcsb 2966 |
. . . 4
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23 | 4 | csbeq1d 2940 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 20, 22, 23 | cbvmpt 3939 |
. . 3
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25 | 19, 24 | syl6eqr 2139 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | eqid 2089 |
. . . 4
![]() ![]() ![]() ![]() | |
27 | nfcvd 2230 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
28 | fmptcof.4 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
29 | 27, 28 | csbiegf 2972 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
30 | 29 | ralimi 2439 |
. . . 4
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31 | mpteq12 3927 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
32 | 26, 30, 31 | sylancr 406 |
. . 3
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33 | 1, 32 | syl 14 |
. 2
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34 | 25, 33 | eqtrd 2121 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-pow 4015 ax-pr 4045 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-eu 1952 df-mo 1953 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ral 2365 df-rex 2366 df-rab 2369 df-v 2622 df-sbc 2842 df-csb 2935 df-un 3004 df-in 3006 df-ss 3013 df-pw 3435 df-sn 3456 df-pr 3457 df-op 3459 df-uni 3660 df-br 3852 df-opab 3906 df-mpt 3907 df-id 4129 df-xp 4457 df-rel 4458 df-cnv 4459 df-co 4460 df-dm 4461 df-rn 4462 df-res 4463 df-ima 4464 df-iota 4993 df-fun 5030 df-fn 5031 df-f 5032 df-fv 5036 |
This theorem is referenced by: fmptcos 5480 |
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