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Theorem reldmtng 24154
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 24100 . 2 toNrmGrp = (𝑔 ∈ V, 𝑓 ∈ V ↦ ((𝑔 sSet ⟨(distβ€˜ndx), (𝑓 ∘ (-gβ€˜π‘”))⟩) sSet ⟨(TopSetβ€˜ndx), (MetOpenβ€˜(𝑓 ∘ (-gβ€˜π‘”)))⟩))
21reldmmpo 7545 1 Rel dom toNrmGrp
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3474  βŸ¨cop 4634  dom cdm 5676   ∘ ccom 5680  Rel wrel 5681  β€˜cfv 6543  (class class class)co 7411   sSet csts 17098  ndxcnx 17128  TopSetcts 17205  distcds 17208  -gcsg 18823  MetOpencmopn 20940   toNrmGrp ctng 24094
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2703  ax-sep 5299  ax-nul 5306  ax-pr 5427
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-nf 1786  df-sb 2068  df-mo 2534  df-eu 2563  df-clab 2710  df-cleq 2724  df-clel 2810  df-nfc 2885  df-rab 3433  df-v 3476  df-dif 3951  df-un 3953  df-in 3955  df-ss 3965  df-nul 4323  df-if 4529  df-sn 4629  df-pr 4631  df-op 4635  df-br 5149  df-opab 5211  df-xp 5682  df-rel 5683  df-dm 5686  df-oprab 7415  df-mpo 7416  df-tng 24100
This theorem is referenced by:  tnglem  24156  tnglemOLD  24157  tngds  24171  tngdsOLD  24172  tcphval  24742
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