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Theorem reldmtng 24368
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 24314 . 2 toNrmGrp = (𝑔 ∈ V, 𝑓 ∈ V ↦ ((𝑔 sSet ⟨(distβ€˜ndx), (𝑓 ∘ (-gβ€˜π‘”))⟩) sSet ⟨(TopSetβ€˜ndx), (MetOpenβ€˜(𝑓 ∘ (-gβ€˜π‘”)))⟩))
21reldmmpo 7546 1 Rel dom toNrmGrp
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3473  βŸ¨cop 4635  dom cdm 5677   ∘ ccom 5681  Rel wrel 5682  β€˜cfv 6544  (class class class)co 7412   sSet csts 17101  ndxcnx 17131  TopSetcts 17208  distcds 17211  -gcsg 18858  MetOpencmopn 21135   toNrmGrp ctng 24308
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-10 2136  ax-11 2153  ax-12 2170  ax-ext 2702  ax-sep 5300  ax-nul 5307  ax-pr 5428
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1781  df-nf 1785  df-sb 2067  df-mo 2533  df-eu 2562  df-clab 2709  df-cleq 2723  df-clel 2809  df-nfc 2884  df-rab 3432  df-v 3475  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 7416  df-mpo 7417  df-tng 24314
This theorem is referenced by:  tnglem  24370  tnglemOLD  24371  tngds  24385  tngdsOLD  24386  tcphval  24967
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