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Theorem reldmtng 18206
Description: The function toNrmGrp is a two-argument function. (Contributed by Mario Carneiro, 8-Oct-2015.)
Assertion
Ref Expression
reldmtng  |-  Rel  dom toNrmGrp

Proof of Theorem reldmtng
Dummy variables  f 
g are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-tng 18159 . 2  |- toNrmGrp  =  ( g  e.  _V , 
f  e.  _V  |->  ( ( g sSet  <. ( dist `  ndx ) ,  ( f  o.  ( -g `  g ) )
>. ) sSet  <. (TopSet `  ndx ) ,  ( MetOpen `  ( f  o.  ( -g `  g ) ) ) >. ) )
21reldmmpt2 5997 1  |-  Rel  dom toNrmGrp
Colors of variables: wff set class
Syntax hints:   _Vcvv 2822   <.cop 3677   dom cdm 4726    o. ccom 4730   Rel wrel 4731   ` cfv 5292  (class class class)co 5900   ndxcnx 13192   sSet csts 13193  TopSetcts 13261   distcds 13264   -gcsg 14414   MetOpencmopn 16423   toNrmGrp ctng 18153
This theorem is referenced by:  tnglem  18208  tngds  18216  tchval  18703
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-14 1705  ax-6 1720  ax-7 1725  ax-11 1732  ax-12 1897  ax-ext 2297  ax-sep 4178  ax-nul 4186  ax-pr 4251
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1533  df-nf 1536  df-sb 1640  df-eu 2180  df-mo 2181  df-clab 2303  df-cleq 2309  df-clel 2312  df-nfc 2441  df-ne 2481  df-ral 2582  df-rex 2583  df-rab 2586  df-v 2824  df-dif 3189  df-un 3191  df-in 3193  df-ss 3200  df-nul 3490  df-if 3600  df-sn 3680  df-pr 3681  df-op 3683  df-br 4061  df-opab 4115  df-xp 4732  df-rel 4733  df-dm 4736  df-oprab 5904  df-mpt2 5905  df-tng 18159
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