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| Mirrors > Home > ILE Home > Th. List > fmpttd | Unicode version | ||
| Description: Version of fmptd 5733 with inlined definition. Domain and codomain of the mapping operation; deduction form. (Contributed by Glauco Siliprandi, 23-Oct-2021.) (Proof shortened by BJ, 16-Aug-2022.) |
| Ref | Expression |
|---|---|
| fmpttd.1 |
|
| Ref | Expression |
|---|---|
| fmpttd |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | fmpttd.1 |
. 2
| |
| 2 | eqid 2204 |
. 2
| |
| 3 | 1, 2 | fmptd 5733 |
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 1469 ax-7 1470 ax-gen 1471 ax-ie1 1515 ax-ie2 1516 ax-8 1526 ax-10 1527 ax-11 1528 ax-i12 1529 ax-bndl 1531 ax-4 1532 ax-17 1548 ax-i9 1552 ax-ial 1556 ax-i5r 1557 ax-14 2178 ax-ext 2186 ax-sep 4161 ax-pow 4217 ax-pr 4252 |
| This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1375 df-nf 1483 df-sb 1785 df-eu 2056 df-mo 2057 df-clab 2191 df-cleq 2197 df-clel 2200 df-nfc 2336 df-ral 2488 df-rex 2489 df-rab 2492 df-v 2773 df-sbc 2998 df-un 3169 df-in 3171 df-ss 3178 df-pw 3617 df-sn 3638 df-pr 3639 df-op 3641 df-uni 3850 df-br 4044 df-opab 4105 df-mpt 4106 df-id 4339 df-xp 4680 df-rel 4681 df-cnv 4682 df-co 4683 df-dm 4684 df-rn 4685 df-res 4686 df-ima 4687 df-iota 5231 df-fun 5272 df-fn 5273 df-f 5274 df-fv 5278 |
| This theorem is referenced by: fmpt3d 5735 pw2f1odclem 6930 ctmlemr 7209 ctssdclemn0 7211 ctssdc 7214 infnninf 7225 nnnninf 7227 ismkvnex 7256 seqf1og 10664 ccatcl 11047 fsumf1o 11643 isumss 11644 fisumss 11645 fsumcl2lem 11651 fsumadd 11659 isumclim3 11676 isummulc2 11679 fsummulc2 11701 isumshft 11743 prodfdivap 11800 fprodf1o 11841 prodssdc 11842 fprodssdc 11843 fprodmul 11844 gsumfzz 13269 gsumfzmptfidmadd 13617 gsumfzconst 13619 gsumfzmhm2 13622 srglmhm 13697 srgrmhm 13698 ringlghm 13765 ringrghm 13766 gsumfzfsumlemm 14291 expghmap 14311 fczpsrbag 14375 mplsubgfilemm 14402 tgrest 14583 resttopon 14585 rest0 14593 cnpfval 14609 txcnp 14685 uptx 14688 cnmpt11 14697 bdxmet 14915 cncfmptc 15010 cncfmptid 15011 cdivcncfap 15018 mulcncf 15022 maxcncf 15029 mincncf 15030 ivthreinc 15059 hovercncf 15060 limcmpted 15077 dvfgg 15102 dvcnp2cntop 15113 dvmulxxbr 15116 dvcjbr 15122 dvexp 15125 dvrecap 15127 dvmptclx 15132 dvmptaddx 15133 dvmptmulx 15134 dvmptcjx 15138 dvef 15141 elply2 15149 plyf 15151 elplyd 15155 dvply2g 15180 lgseisenlem3 15491 lgseisenlem4 15492 2omap 15865 subctctexmid 15870 nninffeq 15890 iswomni0 15923 dceqnconst 15932 dcapnconst 15933 |
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