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Mirrors > Home > ILE Home > Th. List > fmptd | Unicode version |
Description: Domain and codomain of the mapping operation; deduction form. (Contributed by Mario Carneiro, 13-Jan-2013.) |
Ref | Expression |
---|---|
fmptd.1 |
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fmptd.2 |
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Ref | Expression |
---|---|
fmptd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fmptd.1 |
. . 3
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2 | 1 | ralrimiva 2550 |
. 2
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3 | fmptd.2 |
. . 3
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4 | 3 | fmpt 5666 |
. 2
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5 | 2, 4 | sylib 122 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4121 ax-pow 4174 ax-pr 4209 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2739 df-sbc 2963 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4004 df-opab 4065 df-mpt 4066 df-id 4293 df-xp 4632 df-rel 4633 df-cnv 4634 df-co 4635 df-dm 4636 df-rn 4637 df-res 4638 df-ima 4639 df-iota 5178 df-fun 5218 df-fn 5219 df-f 5220 df-fv 5224 |
This theorem is referenced by: fmpttd 5671 fmptco 5682 fliftrel 5792 off 6094 caofinvl 6104 fdiagfn 6691 mapxpen 6847 xpmapenlem 6848 updjudhf 7077 enumctlemm 7112 fodjuf 7142 nninfwlporlem 7170 nninfwlpoimlemg 7172 cc2lem 7264 caucvgsrlemf 7790 caucvgsrlemofff 7795 axcaucvglemf 7894 monoord2 10474 iseqf1olemqf 10488 cvg1nlemf 10987 resqrexlemsqa 11028 climcvg1nlem 11352 summodclem2a 11384 crth 12218 eulerthlem1 12221 ctiunctlemf 12433 txcnmpt 13666 txlm 13672 mulc1cncf 13969 addccncf 13979 negcncf 13981 lgsfcl2 14300 nnsf 14636 nninfself 14644 |
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