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Mirrors > Home > MPE Home > Th. List > foima | Structured version Visualization version Unicode version |
Description: The image of the domain of an onto function. (Contributed by NM, 29-Nov-2002.) |
Ref | Expression |
---|---|
foima |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imadmrn 5476 | . 2 | |
2 | fof 6115 | . . . 4 | |
3 | fdm 6051 | . . . 4 | |
4 | 2, 3 | syl 17 | . . 3 |
5 | 4 | imaeq2d 5466 | . 2 |
6 | forn 6118 | . 2 | |
7 | 1, 5, 6 | 3eqtr3a 2680 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wceq 1483 cdm 5114 crn 5115 cima 5117 wf 5884 wfo 5886 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ral 2917 df-rex 2918 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-xp 5120 df-cnv 5122 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-fn 5891 df-f 5892 df-fo 5894 |
This theorem is referenced by: foimacnv 6154 domunfican 8233 fiint 8237 fodomfi 8239 cantnflt2 8570 cantnfp1lem3 8577 enfin1ai 9206 symgfixelsi 17855 dprdf1o 18431 lmimlbs 20175 cncmp 21195 cmpfi 21211 cnconn 21225 qtopval2 21499 elfm3 21754 rnelfm 21757 fmfnfmlem2 21759 fmfnfm 21762 eupthvdres 27095 pjordi 29032 qtophaus 29903 poimirlem1 33410 poimirlem2 33411 poimirlem3 33412 poimirlem4 33413 poimirlem5 33414 poimirlem6 33415 poimirlem7 33416 poimirlem9 33418 poimirlem10 33419 poimirlem11 33420 poimirlem12 33421 poimirlem14 33423 poimirlem16 33425 poimirlem17 33426 poimirlem19 33428 poimirlem20 33429 poimirlem22 33431 poimirlem23 33432 poimirlem24 33433 poimirlem25 33434 poimirlem29 33438 poimirlem31 33440 ovoliunnfl 33451 voliunnfl 33453 volsupnfl 33454 ismtybndlem 33605 kelac1 37633 gicabl 37669 |
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