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Mirrors > Home > ILE Home > Th. List > mptex | Unicode version |
Description: If the domain of a function given by maps-to notation is a set, the function is a set. (Contributed by NM, 22-Apr-2005.) (Revised by Mario Carneiro, 20-Dec-2013.) |
Ref | Expression |
---|---|
mptex.1 |
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Ref | Expression |
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mptex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mptex.1 |
. 2
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2 | mptexg 5762 |
. 2
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3 | 1, 2 | ax-mp 5 |
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-14 2163 ax-ext 2171 ax-coll 4133 ax-sep 4136 ax-pow 4192 ax-pr 4227 |
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-reu 2475 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-f1 5240 df-fo 5241 df-f1o 5242 df-fv 5243 |
This theorem is referenced by: mptrabex 5765 eufnfv 5768 abrexex 6142 ofmres 6161 difinfsn 7129 ctmlemr 7137 ctssdclemn0 7139 ctssdc 7142 enumct 7144 frec2uzrand 10436 frec2uzf1od 10437 frecfzennn 10457 uzennn 10467 0tonninf 10470 1tonninf 10471 hashinfom 10790 absval 11042 climle 11374 climcvg1nlem 11389 iserabs 11515 isumshft 11530 divcnv 11537 trireciplem 11540 expcnvap0 11542 expcnvre 11543 expcnv 11544 explecnv 11545 geolim 11551 geo2lim 11556 mertenslem2 11576 eftlub 11730 1arithlem1 12395 1arith 12399 ctiunct 12491 restfn 12748 zrhval2 13916 peano4nninf 15217 peano3nninf 15218 nninfsellemeq 15225 nninfsellemeqinf 15227 dceqnconst 15270 dcapnconst 15271 |
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