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Mirrors > Home > ILE Home > Th. List > fnmap | Unicode version |
Description: Set exponentiation has a universal domain. (Contributed by NM, 8-Dec-2003.) (Revised by Mario Carneiro, 8-Sep-2013.) |
Ref | Expression |
---|---|
fnmap |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-map 6675 |
. 2
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2 | vex 2755 |
. . 3
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3 | vex 2755 |
. . 3
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4 | mapex 6679 |
. . 3
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5 | 2, 3, 4 | mp2an 426 |
. 2
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6 | 1, 5 | fnmpoi 6228 |
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 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 ax-un 4451 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-eu 2041 df-mo 2042 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-rex 2474 df-rab 2477 df-v 2754 df-sbc 2978 df-csb 3073 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-iun 3903 df-br 4019 df-opab 4080 df-mpt 4081 df-id 4311 df-xp 4650 df-rel 4651 df-cnv 4652 df-co 4653 df-dm 4654 df-rn 4655 df-res 4656 df-ima 4657 df-iota 5196 df-fun 5237 df-fn 5238 df-f 5239 df-fv 5243 df-oprab 5899 df-mpo 5900 df-1st 6164 df-2nd 6165 df-map 6675 |
This theorem is referenced by: mapsnen 6836 map1 6837 mapen 6873 mapdom1g 6874 mapxpen 6875 xpmapenlem 6876 hashfacen 10847 omctfn 12493 ismhm 12910 mhmex 12911 rhmex 13504 cnfval 14146 cnpfval 14147 cnpval 14150 ismet 14296 isxmet 14297 xmetunirn 14310 |
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