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Theorem reldmtng 24147
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 24093 . 2 toNrmGrp = (𝑔 ∈ V, 𝑓 ∈ V ↦ ((𝑔 sSet ⟨(distβ€˜ndx), (𝑓 ∘ (-gβ€˜π‘”))⟩) sSet ⟨(TopSetβ€˜ndx), (MetOpenβ€˜(𝑓 ∘ (-gβ€˜π‘”)))⟩))
21reldmmpo 7543 1 Rel dom toNrmGrp
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3475  βŸ¨cop 4635  dom cdm 5677   ∘ ccom 5681  Rel wrel 5682  β€˜cfv 6544  (class class class)co 7409   sSet csts 17096  ndxcnx 17126  TopSetcts 17203  distcds 17206  -gcsg 18821  MetOpencmopn 20934   toNrmGrp ctng 24087
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-10 2138  ax-11 2155  ax-12 2172  ax-ext 2704  ax-sep 5300  ax-nul 5307  ax-pr 5428
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-3an 1090  df-tru 1545  df-fal 1555  df-ex 1783  df-nf 1787  df-sb 2069  df-mo 2535  df-eu 2564  df-clab 2711  df-cleq 2725  df-clel 2811  df-nfc 2886  df-rab 3434  df-v 3477  df-dif 3952  df-un 3954  df-in 3956  df-ss 3966  df-nul 4324  df-if 4530  df-sn 4630  df-pr 4632  df-op 4636  df-br 5150  df-opab 5212  df-xp 5683  df-rel 5684  df-dm 5687  df-oprab 7413  df-mpo 7414  df-tng 24093
This theorem is referenced by:  tnglem  24149  tnglemOLD  24150  tngds  24164  tngdsOLD  24165  tcphval  24735
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