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Mirrors > Home > MPE Home > Th. List > funimass4 | Structured version Visualization version Unicode version |
Description: Membership relation for the values of a function whose image is a subclass. (Contributed by Raph Levien, 20-Nov-2006.) |
Ref | Expression |
---|---|
funimass4 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfss2 3432 |
. . 3
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2 | eqcom 2468 |
. . . . . . . . . 10
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3 | ssel 3437 |
. . . . . . . . . . . 12
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4 | funbrfvb 5929 |
. . . . . . . . . . . . 13
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 4 | ex 440 |
. . . . . . . . . . . 12
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6 | 3, 5 | syl9 73 |
. . . . . . . . . . 11
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7 | 6 | imp31 438 |
. . . . . . . . . 10
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8 | 2, 7 | syl5bb 265 |
. . . . . . . . 9
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9 | 8 | rexbidva 2909 |
. . . . . . . 8
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10 | vex 3059 |
. . . . . . . . 9
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11 | 10 | elima 5191 |
. . . . . . . 8
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12 | 9, 11 | syl6rbbr 272 |
. . . . . . 7
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13 | 12 | imbi1d 323 |
. . . . . 6
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14 | r19.23v 2878 |
. . . . . 6
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15 | 13, 14 | syl6bbr 271 |
. . . . 5
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16 | 15 | albidv 1777 |
. . . 4
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17 | ralcom4 3077 |
. . . . 5
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18 | fvex 5897 |
. . . . . . 7
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19 | eleq1 2527 |
. . . . . . 7
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20 | 18, 19 | ceqsalv 3086 |
. . . . . 6
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21 | 20 | ralbii 2830 |
. . . . 5
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22 | 17, 21 | bitr3i 259 |
. . . 4
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23 | 16, 22 | syl6bb 269 |
. . 3
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24 | 1, 23 | syl5bb 265 |
. 2
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25 | 24 | ancoms 459 |
1
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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-9 1906 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 ax-sep 4538 ax-nul 4547 ax-pr 4652 |
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-rab 2757 df-v 3058 df-sbc 3279 df-dif 3418 df-un 3420 df-in 3422 df-ss 3429 df-nul 3743 df-if 3893 df-sn 3980 df-pr 3982 df-op 3986 df-uni 4212 df-br 4416 df-opab 4475 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-fv 5608 |
This theorem is referenced by: funimass3 6020 funimass5 6021 funconstss 6022 funimassov 6472 fnwelem 6937 cnfcomlem 8229 dfac12lem2 8599 ackbij1b 8694 wunom 9170 phimullem 14775 frmdss2 16695 cntzmhm2 17041 dprd2da 17723 frlmsslsp 19402 1stckgenlem 20616 txcnp 20683 ptcnplem 20684 xkopt 20718 xkoinjcn 20750 tgqtop 20775 uzrest 20960 cnflf2 21066 lmflf 21068 txflf 21069 cnextcn 21130 ghmcnp 21177 ucnima 21344 metcnp 21604 tchcph 22259 ovolficcss 22470 opnmbllem 22607 ellimc2 22880 ellimc3 22882 deg1n0ima 23086 dvloglem 23641 logf1o2 23643 dchrghm 24232 usgrares1 25186 xrofsup 28401 eulerpartlemd 29247 erdszelem2 29963 cvmlift3lem7 30096 mclsax 30255 filnetlem4 31085 poimir 32017 opnmbllem0 32020 cnres2 32139 icccncfext 37802 |
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