![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > fmpttd | Unicode version |
Description: Version of fmptd 5672 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 2177 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 1, 2 | fmptd 5672 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 4123 ax-pow 4176 ax-pr 4211 |
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 2741 df-sbc 2965 df-un 3135 df-in 3137 df-ss 3144 df-pw 3579 df-sn 3600 df-pr 3601 df-op 3603 df-uni 3812 df-br 4006 df-opab 4067 df-mpt 4068 df-id 4295 df-xp 4634 df-rel 4635 df-cnv 4636 df-co 4637 df-dm 4638 df-rn 4639 df-res 4640 df-ima 4641 df-iota 5180 df-fun 5220 df-fn 5221 df-f 5222 df-fv 5226 |
This theorem is referenced by: fmpt3d 5674 ctmlemr 7109 ctssdclemn0 7111 ctssdc 7114 infnninf 7124 nnnninf 7126 ismkvnex 7155 fsumf1o 11400 isumss 11401 fisumss 11402 fsumcl2lem 11408 fsumadd 11416 isumclim3 11433 isummulc2 11436 fsummulc2 11458 isumshft 11500 prodfdivap 11557 fprodf1o 11598 prodssdc 11599 fprodssdc 11600 fprodmul 11601 srglmhm 13181 srgrmhm 13182 tgrest 13754 resttopon 13756 rest0 13764 cnpfval 13780 txcnp 13856 uptx 13859 cnmpt11 13868 bdxmet 14086 cncfmptc 14167 cncfmptid 14168 cdivcncfap 14172 mulcncf 14176 limcmpted 14217 dvfgg 14242 dvcnp2cntop 14248 dvmulxxbr 14251 dvcjbr 14257 dvexp 14260 dvrecap 14262 dvmptclx 14265 dvmptaddx 14266 dvmptmulx 14267 dvmptcjx 14271 dvef 14273 subctctexmid 14835 nninffeq 14854 iswomni0 14884 dceqnconst 14893 dcapnconst 14894 |
Copyright terms: Public domain | W3C validator |