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Mirrors > Home > ILE Home > Th. List > fmpttd | Unicode version |
Description: Version of fmptd 5542 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 2117 | . 2 | |
3 | 1, 2 | fmptd 5542 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1465 cmpt 3959 wf 5089 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-sbc 2883 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-br 3900 df-opab 3960 df-mpt 3961 df-id 4185 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 df-iota 5058 df-fun 5095 df-fn 5096 df-f 5097 df-fv 5101 |
This theorem is referenced by: fmpt3d 5544 ctmlemr 6961 ctssdclemn0 6963 ctssdc 6966 ismkvnex 6997 fsumf1o 11114 isumss 11115 fisumss 11116 fsumcl2lem 11122 fsumadd 11130 isumclim3 11147 isummulc2 11150 fsummulc2 11172 isumshft 11214 tgrest 12249 resttopon 12251 rest0 12259 cnpfval 12275 txcnp 12351 uptx 12354 cnmpt11 12363 bdxmet 12581 cncfmptc 12662 cncfmptid 12663 cdivcncfap 12667 mulcncf 12671 limcmpted 12712 dvfgg 12737 dvcnp2cntop 12743 dvmulxxbr 12746 dvcjbr 12752 dvexp 12755 dvrecap 12757 dvmptclx 12760 dvmptaddx 12761 dvmptmulx 12762 dvef 12767 subctctexmid 13092 nninffeq 13112 |
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