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Mirrors > Home > ILE Home > Th. List > fmpo | Unicode version |
Description: Functionality, domain and range of a class given by the maps-to notation. (Contributed by FL, 17-May-2010.) |
Ref | Expression |
---|---|
fmpo.1 |
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Ref | Expression |
---|---|
fmpo |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fmpo.1 |
. . 3
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2 | 1 | fmpox 6106 |
. 2
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3 | iunxpconst 4607 |
. . 3
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4 | 3 | feq2i 5274 |
. 2
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5 | 2, 4 | bitri 183 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 ax-pow 4106 ax-pr 4139 ax-un 4363 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-mo 2004 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 df-rab 2426 df-v 2691 df-sbc 2914 df-csb 3008 df-un 3080 df-in 3082 df-ss 3089 df-pw 3517 df-sn 3538 df-pr 3539 df-op 3541 df-uni 3745 df-iun 3823 df-br 3938 df-opab 3998 df-mpt 3999 df-id 4223 df-xp 4553 df-rel 4554 df-cnv 4555 df-co 4556 df-dm 4557 df-rn 4558 df-res 4559 df-ima 4560 df-iota 5096 df-fun 5133 df-fn 5134 df-f 5135 df-fv 5139 df-oprab 5786 df-mpo 5787 df-1st 6046 df-2nd 6047 |
This theorem is referenced by: fnmpo 6108 ovmpoelrn 6113 fmpoco 6121 eroprf 6530 mapxpen 6750 subf 7988 xaddf 9657 ixxf 9711 ioof 9784 fzf 9825 fzof 9952 gcdf 11697 eucalgf 11772 txuni2 12464 txbasval 12475 cnmpt12 12495 cnmpt21 12499 cnmpt2t 12501 cnmpt22 12502 cnmptcom 12506 txswaphmeo 12529 blfvalps 12593 blfps 12617 blf 12618 bdmet 12710 xmetxp 12715 |
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