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Mirrors > Home > MPE Home > Th. List > foimacnv | Structured version Visualization version Unicode version |
Description: A reverse version of f1imacnv 5857. (Contributed by Jeff Hankins, 16-Jul-2009.) |
Ref | Expression |
---|---|
foimacnv |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resima 5159 |
. 2
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2 | fofun 5821 |
. . . . . 6
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3 | 2 | adantr 471 |
. . . . 5
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4 | funcnvres2 5680 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | 3, 4 | syl 17 |
. . . 4
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6 | 5 | imaeq1d 5189 |
. . 3
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7 | resss 5150 |
. . . . . . . . . . 11
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8 | cnvss 5029 |
. . . . . . . . . . 11
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9 | 7, 8 | ax-mp 5 |
. . . . . . . . . 10
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10 | cnvcnvss 5313 |
. . . . . . . . . 10
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11 | 9, 10 | sstri 3453 |
. . . . . . . . 9
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12 | funss 5623 |
. . . . . . . . 9
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13 | 11, 2, 12 | mpsyl 65 |
. . . . . . . 8
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14 | 13 | adantr 471 |
. . . . . . 7
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15 | df-ima 4869 |
. . . . . . . 8
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16 | df-rn 4867 |
. . . . . . . 8
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17 | 15, 16 | eqtr2i 2485 |
. . . . . . 7
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18 | 14, 17 | jctir 545 |
. . . . . 6
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19 | df-fn 5608 |
. . . . . 6
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20 | 18, 19 | sylibr 217 |
. . . . 5
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21 | dfdm4 5049 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
22 | forn 5823 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
23 | 22 | sseq2d 3472 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 23 | biimpar 492 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | df-rn 4867 |
. . . . . . . 8
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26 | 24, 25 | syl6sseq 3490 |
. . . . . . 7
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27 | ssdmres 5148 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
28 | 26, 27 | sylib 201 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
29 | 21, 28 | syl5eqr 2510 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
30 | df-fo 5611 |
. . . . 5
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31 | 20, 29, 30 | sylanbrc 675 |
. . . 4
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32 | foima 5825 |
. . . 4
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33 | 31, 32 | syl 17 |
. . 3
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34 | 6, 33 | eqtr3d 2498 |
. 2
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35 | 1, 34 | syl5eqr 2510 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-sep 4541 ax-nul 4550 ax-pr 4656 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rex 2755 df-rab 2758 df-v 3059 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-sn 3981 df-pr 3983 df-op 3987 df-br 4419 df-opab 4478 df-id 4771 df-xp 4862 df-rel 4863 df-cnv 4864 df-co 4865 df-dm 4866 df-rn 4867 df-res 4868 df-ima 4869 df-fun 5607 df-fn 5608 df-f 5609 df-fo 5611 |
This theorem is referenced by: f1opw2 6554 imacosupp 6987 fopwdom 7711 f1opwfi 7909 enfin2i 8782 fin1a2lem7 8867 fsumss 13846 fprodss 14057 gicsubgen 16997 coe1mul2lem2 18916 cncmp 20462 cnconn 20492 qtoprest 20787 qtopomap 20788 qtopcmap 20789 hmeoimaf1o 20840 elfm3 21020 imasf1oxms 21559 mbfimaopnlem 22667 cvmsss2 30047 diaintclN 34672 dibintclN 34781 dihintcl 34958 lnmepi 35989 pwfi2f1o 36000 sge0f1o 38327 |
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