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Theorem reldmnghm 18707
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 18704 . 2  |- NGHom  =  ( s  e. NrmGrp ,  t  e. NrmGrp  |->  ( `' ( s
normOp t ) " RR ) )
21reldmmpt2 6148 1  |-  Rel  dom NGHom
Colors of variables: wff set class
Syntax hints:   `'ccnv 4844   dom cdm 4845   "cima 4848   Rel wrel 4850  (class class class)co 6048   RRcr 8953  NrmGrpcngp 18586   normOpcnmo 18700   NGHom cnghm 18701
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393  ax-sep 4298  ax-nul 4306  ax-pr 4371
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2266  df-mo 2267  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-ne 2577  df-ral 2679  df-rex 2680  df-rab 2683  df-v 2926  df-dif 3291  df-un 3293  df-in 3295  df-ss 3302  df-nul 3597  df-if 3708  df-sn 3788  df-pr 3789  df-op 3791  df-br 4181  df-opab 4235  df-xp 4851  df-rel 4852  df-dm 4855  df-oprab 6052  df-mpt2 6053  df-nghm 18704
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