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Theorem reldmtng 18679
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 18632 . 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 6181 1  |-  Rel  dom toNrmGrp
Colors of variables: wff set class
Syntax hints:   _Vcvv 2956   <.cop 3817   dom cdm 4878    o. ccom 4882   Rel wrel 4883   ` cfv 5454  (class class class)co 6081   ndxcnx 13466   sSet csts 13467  TopSetcts 13535   distcds 13538   -gcsg 14688   MetOpencmopn 16691   toNrmGrp ctng 18626
This theorem is referenced by:  tnglem  18681  tngds  18689  tchval  19177
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-mo 2286  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-br 4213  df-opab 4267  df-xp 4884  df-rel 4885  df-dm 4888  df-oprab 6085  df-mpt2 6086  df-tng 18632
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