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Mirrors > Home > ILE Home > Th. List > fmpttd | Unicode version |
Description: Version of fmptd 5528 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 |
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fmpttd.1 |
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Ref | Expression |
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fmpttd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fmpttd.1 |
. 2
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2 | eqid 2115 |
. 2
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3 | 1, 2 | fmptd 5528 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-14 1475 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 ax-sep 4006 ax-pow 4058 ax-pr 4091 |
This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-nf 1420 df-sb 1719 df-eu 1978 df-mo 1979 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-ral 2395 df-rex 2396 df-rab 2399 df-v 2659 df-sbc 2879 df-un 3041 df-in 3043 df-ss 3050 df-pw 3478 df-sn 3499 df-pr 3500 df-op 3502 df-uni 3703 df-br 3896 df-opab 3950 df-mpt 3951 df-id 4175 df-xp 4505 df-rel 4506 df-cnv 4507 df-co 4508 df-dm 4509 df-rn 4510 df-res 4511 df-ima 4512 df-iota 5046 df-fun 5083 df-fn 5084 df-f 5085 df-fv 5089 |
This theorem is referenced by: fmpt3d 5530 ctmlemr 6945 ctssdclemn0 6947 ctssdc 6950 ismkvnex 6979 fsumf1o 11051 isumss 11052 fisumss 11053 fsumcl2lem 11059 fsumadd 11067 isumclim3 11084 isummulc2 11087 fsummulc2 11109 isumshft 11151 tgrest 12181 resttopon 12183 rest0 12191 cnpfval 12207 txcnp 12282 uptx 12285 cnmpt11 12294 bdxmet 12490 cncfmptc 12568 cncfmptid 12569 cdivcncfap 12573 mulcncf 12577 limcmpted 12588 dvfgg 12612 dvcnp2cntop 12618 dvmulxxbr 12621 subctctexmid 12888 nninffeq 12908 |
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