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Theorem reldmnghm 18777
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 18774 . 2  |- NGHom  =  ( s  e. NrmGrp ,  t  e. NrmGrp  |->  ( `' ( s
normOp t ) " RR ) )
21reldmmpt2 6210 1  |-  Rel  dom NGHom
Colors of variables: wff set class
Syntax hints:   `'ccnv 4906   dom cdm 4907   "cima 4910   Rel wrel 4912  (class class class)co 6110   RRcr 9020  NrmGrpcngp 18656   normOpcnmo 18770   NGHom cnghm 18771
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-sep 4355  ax-nul 4363  ax-pr 4432
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2291  df-mo 2292  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-rex 2717  df-rab 2720  df-v 2964  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-br 4238  df-opab 4292  df-xp 4913  df-rel 4914  df-dm 4917  df-oprab 6114  df-mpt2 6115  df-nghm 18774
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