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Mirrors > Home > ILE Home > Th. List > fmptcof | Unicode version |
Description: Version of fmptco 5503 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 2977 |
. . . . . . 7
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3 | 2 | nfel1 2246 |
. . . . . 6
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4 | csbeq1a 2955 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 4 | eleq1d 2163 |
. . . . . 6
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6 | 3, 5 | rspc 2730 |
. . . . 5
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7 | 1, 6 | mpan9 276 |
. . . 4
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8 | fmptcof.2 |
. . . . 5
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9 | nfcv 2235 |
. . . . . 6
![]() ![]() ![]() ![]() | |
10 | 9, 2, 4 | cbvmpt 3955 |
. . . . 5
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11 | 8, 10 | syl6eq 2143 |
. . . 4
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12 | fmptcof.3 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
13 | nfcv 2235 |
. . . . . 6
![]() ![]() ![]() ![]() | |
14 | nfcsb1v 2977 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | csbeq1a 2955 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
16 | 13, 14, 15 | cbvmpt 3955 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 12, 16 | syl6eq 2143 |
. . . 4
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18 | csbeq1 2950 |
. . . 4
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19 | 7, 11, 17, 18 | fmptco 5503 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | nfcv 2235 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | nfcv 2235 |
. . . . 5
![]() ![]() ![]() ![]() | |
22 | 2, 21 | nfcsb 2979 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 4 | csbeq1d 2953 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 20, 22, 23 | cbvmpt 3955 |
. . 3
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25 | 19, 24 | syl6eqr 2145 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | eqid 2095 |
. . . 4
![]() ![]() ![]() ![]() | |
27 | nfcvd 2236 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
28 | fmptcof.4 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
29 | 27, 28 | csbiegf 2985 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
30 | 29 | ralimi 2449 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
31 | mpteq12 3943 |
. . . 4
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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 2127 |
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 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-bndl 1451 ax-4 1452 ax-14 1457 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 ax-ext 2077 ax-sep 3978 ax-pow 4030 ax-pr 4060 |
This theorem depends on definitions: df-bi 116 df-3an 929 df-tru 1299 df-nf 1402 df-sb 1700 df-eu 1958 df-mo 1959 df-clab 2082 df-cleq 2088 df-clel 2091 df-nfc 2224 df-ral 2375 df-rex 2376 df-rab 2379 df-v 2635 df-sbc 2855 df-csb 2948 df-un 3017 df-in 3019 df-ss 3026 df-pw 3451 df-sn 3472 df-pr 3473 df-op 3475 df-uni 3676 df-br 3868 df-opab 3922 df-mpt 3923 df-id 4144 df-xp 4473 df-rel 4474 df-cnv 4475 df-co 4476 df-dm 4477 df-rn 4478 df-res 4479 df-ima 4480 df-iota 5014 df-fun 5051 df-fn 5052 df-f 5053 df-fv 5057 |
This theorem is referenced by: fmptcos 5505 |
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