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Theorem reldmtng 18154
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 18107 . 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 5955 1  |-  Rel  dom toNrmGrp
Colors of variables: wff set class
Syntax hints:   _Vcvv 2788   <.cop 3643   dom cdm 4689    o. ccom 4693   Rel wrel 4694   ` cfv 5255  (class class class)co 5858   ndxcnx 13145   sSet csts 13146  TopSetcts 13214   distcds 13217   -gcsg 14365   MetOpencmopn 16372   toNrmGrp ctng 18101
This theorem is referenced by:  tnglem  18156  tngds  18164  tchval  18650
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-tng 18107
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