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Theorem hicli 21660
Description: Closure inference for inner product. (Contributed by NM, 1-Aug-1999.) (New usage is discouraged.)
Hypotheses
Ref Expression
hicl.1  |-  A  e. 
~H
hicl.2  |-  B  e. 
~H
Assertion
Ref Expression
hicli  |-  ( A 
.ih  B )  e.  CC

Proof of Theorem hicli
StepHypRef Expression
1 hicl.1 . 2  |-  A  e. 
~H
2 hicl.2 . 2  |-  B  e. 
~H
3 hicl 21659 . 2  |-  ( ( A  e.  ~H  /\  B  e.  ~H )  ->  ( A  .ih  B
)  e.  CC )
41, 2, 3mp2an 653 1  |-  ( A 
.ih  B )  e.  CC
Colors of variables: wff set class
Syntax hints:    e. wcel 1684  (class class class)co 5858   CCcc 8735   ~Hchil 21499    .ih csp 21502
This theorem is referenced by:  hisubcomi  21683  normlem0  21688  normlem2  21690  normlem3  21691  normlem7  21695  normlem8  21696  normlem9  21697  bcseqi  21699  norm-ii-i  21716  normpythi  21721  normpari  21733  polid2i  21736  bcsiALT  21758  h1de2i  22132  h1de2bi  22133  h1de2ctlem  22134  eigrei  22414  eigorthi  22417  lnopunilem1  22590  lnopunilem2  22591
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214  ax-hfi 21658
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-mo 2148  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-rab 2552  df-v 2790  df-sbc 2992  df-csb 3082  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-iun 3907  df-br 4024  df-opab 4078  df-mpt 4079  df-id 4309  df-xp 4695  df-rel 4696  df-cnv 4697  df-co 4698  df-dm 4699  df-rn 4700  df-iota 5219  df-fun 5257  df-fn 5258  df-f 5259  df-fv 5263  df-ov 5861
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