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Theorem reldmnghm 18221
Description: Lemma for normed group homomorphisms. (Contributed by Mario Carneiro, 18-Oct-2015.)
Assertion
Ref Expression
reldmnghm  |-  Rel  dom NGHom

Proof of Theorem reldmnghm
Dummy variables  s 
t are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-nghm 18218 . 2  |- NGHom  =  ( s  e. NrmGrp ,  t  e. NrmGrp  |->  ( `' ( s
normOp t ) " RR ) )
21reldmmpt2 5955 1  |-  Rel  dom NGHom
Colors of variables: wff set class
Syntax hints:   `'ccnv 4688   dom cdm 4689   "cima 4692   Rel wrel 4694  (class class class)co 5858   RRcr 8736  NrmGrpcngp 18100   normOpcnmo 18214   NGHom cnghm 18215
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
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-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-br 4024  df-opab 4078  df-xp 4695  df-rel 4696  df-dm 4699  df-oprab 5862  df-mpt2 5863  df-nghm 18218
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