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Mirrors > Home > MPE Home > Th. List > cnextfval | Structured version Visualization version Unicode version |
Description: The continuous extension
of a given function ![]() |
Ref | Expression |
---|---|
cnextfval.1 |
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cnextfval.2 |
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Ref | Expression |
---|---|
cnextfval |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnextval 21124 |
. . 3
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2 | 1 | adantr 471 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | simpr 467 |
. . . . . 6
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4 | 3 | dmeqd 5055 |
. . . . 5
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5 | simplrl 775 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | fdm 5755 |
. . . . . 6
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7 | 5, 6 | syl 17 |
. . . . 5
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8 | 4, 7 | eqtrd 2495 |
. . . 4
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9 | 8 | fveq2d 5891 |
. . 3
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10 | 8 | oveq2d 6330 |
. . . . . 6
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11 | 10 | oveq2d 6330 |
. . . . 5
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12 | 11, 3 | fveq12d 5893 |
. . . 4
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13 | 12 | xpeq2d 4876 |
. . 3
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14 | 9, 13 | iuneq12d 4317 |
. 2
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15 | uniexg 6614 |
. . . 4
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16 | 15 | ad2antlr 738 |
. . 3
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17 | uniexg 6614 |
. . . 4
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18 | 17 | ad2antrr 737 |
. . 3
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19 | eqid 2461 |
. . . . . 6
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20 | cnextfval.2 |
. . . . . 6
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21 | 19, 20 | feq23i 5744 |
. . . . 5
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22 | 21 | biimpi 199 |
. . . 4
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23 | 22 | ad2antrl 739 |
. . 3
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24 | cnextfval.1 |
. . . . . 6
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25 | 24 | sseq2i 3468 |
. . . . 5
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26 | 25 | biimpi 199 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | 26 | ad2antll 740 |
. . 3
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28 | elpm2r 7514 |
. . 3
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29 | 16, 18, 23, 27, 28 | syl22anc 1277 |
. 2
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30 | fvex 5897 |
. . . 4
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31 | snex 4654 |
. . . . 5
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32 | fvex 5897 |
. . . . 5
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33 | 31, 32 | xpex 6621 |
. . . 4
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34 | 30, 33 | iunex 6799 |
. . 3
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35 | 34 | a1i 11 |
. 2
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36 | 2, 14, 29, 35 | fvmptd 5976 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-8 1899 ax-9 1906 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 ax-rep 4528 ax-sep 4538 ax-nul 4547 ax-pow 4594 ax-pr 4652 ax-un 6609 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-eu 2313 df-mo 2314 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-ne 2634 df-ral 2753 df-rex 2754 df-reu 2755 df-rab 2757 df-v 3058 df-sbc 3279 df-csb 3375 df-dif 3418 df-un 3420 df-in 3422 df-ss 3429 df-nul 3743 df-if 3893 df-pw 3964 df-sn 3980 df-pr 3982 df-op 3986 df-uni 4212 df-iun 4293 df-br 4416 df-opab 4475 df-mpt 4476 df-id 4767 df-xp 4858 df-rel 4859 df-cnv 4860 df-co 4861 df-dm 4862 df-rn 4863 df-res 4864 df-ima 4865 df-iota 5564 df-fun 5602 df-fn 5603 df-f 5604 df-f1 5605 df-fo 5606 df-f1o 5607 df-fv 5608 df-ov 6317 df-oprab 6318 df-mpt2 6319 df-pm 7500 df-cnext 21123 |
This theorem is referenced by: cnextrel 21126 cnextfun 21127 cnextfvval 21128 cnextf 21129 cnextfres 21132 |
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