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Theorem hdmapfnN 32644
 Description: Functionality of map from vectors to functionals with closed kernels. (Contributed by NM, 30-May-2015.) (New usage is discouraged.)
Hypotheses
Ref Expression
hdmapfn.h
hdmapfn.u
hdmapfn.v
hdmapfn.s HDMap
hdmapfn.k
Assertion
Ref Expression
hdmapfnN

Proof of Theorem hdmapfnN
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 riotaex 6324 . . 3 LCDual HDMap1 HDMap1 HVMap
2 eqid 2296 . . 3 LCDual HDMap1 HDMap1 HVMap LCDual HDMap1 HDMap1 HVMap
31, 2fnmpti 5388 . 2 LCDual HDMap1 HDMap1 HVMap
4 hdmapfn.h . . . 4
5 eqid 2296 . . . 4
6 hdmapfn.u . . . 4
7 hdmapfn.v . . . 4
8 eqid 2296 . . . 4
9 eqid 2296 . . . 4 LCDual LCDual
10 eqid 2296 . . . 4 LCDual LCDual
11 eqid 2296 . . . 4 HVMap HVMap
12 eqid 2296 . . . 4 HDMap1 HDMap1
13 hdmapfn.s . . . 4 HDMap
14 hdmapfn.k . . . 4
154, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14hdmapfval 32642 . . 3 LCDual HDMap1 HDMap1 HVMap
1615fneq1d 5351 . 2 LCDual HDMap1 HDMap1 HVMap
173, 16mpbiri 224 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 358   wceq 1632   wcel 1696  wral 2556   cun 3163  csn 3653  cop 3656  cotp 3657   cmpt 4093   cid 4320   cres 4707   wfn 5266  cfv 5271  crio 6313  cbs 13164  clspn 15744  chlt 30162  clh 30795  cltrn 30912  cdvh 31890  LCDualclcd 32398  HVMapchvm 32568  HDMap1chdma1 32604  HDMapchdma 32605 This theorem is referenced by:  hdmaprnlem11N  32675  hdmaprnlem17N  32678  hdmaprnN  32679  hdmapf1oN  32680  hgmaprnlem4N  32714 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-rep 4147  ax-sep 4157  ax-nul 4165  ax-pr 4230 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-mo 2161  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-reu 2563  df-rab 2565  df-v 2803  df-sbc 3005  df-csb 3095  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-ot 3663  df-uni 3844  df-iun 3923  df-br 4040  df-opab 4094  df-mpt 4095  df-id 4325  df-xp 4711  df-rel 4712  df-cnv 4713  df-co 4714  df-dm 4715  df-rn 4716  df-res 4717  df-ima 4718  df-iota 5235  df-fun 5273  df-fn 5274  df-f 5275  df-f1 5276  df-fo 5277  df-f1o 5278  df-fv 5279  df-riota 6320  df-hdmap 32607
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