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Mirrors > Home > MPE Home > Th. List > funfvima2 | Structured version Visualization version Unicode version |
Description: A function's value in an included preimage belongs to the image. (Contributed by NM, 3-Feb-1997.) |
Ref | Expression |
---|---|
funfvima2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 3437 |
. . 3
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2 | funfvima 6164 |
. . . . . 6
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3 | 2 | ex 440 |
. . . . 5
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4 | 3 | com23 81 |
. . . 4
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5 | 4 | a2d 29 |
. . 3
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6 | 1, 5 | syl5 33 |
. 2
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7 | 6 | imp 435 |
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: fnfvima 6167 f1oweALT 6803 tz7.49 7187 phimullem 14775 mrcuni 15575 frlmsslsp 19402 lindfrn 19427 iscldtop 20159 1stcfb 20508 2ndcomap 20521 rnelfm 21016 fmfnfmlem2 21018 fmfnfmlem4 21020 qtopbaslem 21827 tgqioo 21866 bndth 22034 volsup 22557 dyadmbllem 22605 opnmbllem 22607 itg1addlem4 22705 c1liplem1 22996 dvcnvrelem1 23017 dvcnvrelem2 23018 plyco0 23194 plyaddlem1 23215 plymullem1 23216 dvloglem 23641 logf1o2 23643 efopn 23651 axcontlem10 25051 eupares 25751 imaelshi 27759 funimass4f 28282 sitgclg 29223 cvmliftlem3 30058 nocvxminlem 30627 nocvxmin 30628 ivthALT 31039 opnmbllem0 32020 ismtyres 32184 heibor1lem 32185 ismrc 35587 aomclem4 35959 funfvima2d 36656 |
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