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Theorem reldmghm 17706
Description: Lemma for group homomorphisms. (Contributed by Stefan O'Rear, 31-Dec-2014.)
Assertion
Ref Expression
reldmghm Rel dom GrpHom

Proof of Theorem reldmghm
Dummy variables 𝑔 𝑠 𝑡 𝑤 𝑥 𝑦 are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 df-ghm 17705 . 2 GrpHom = (𝑠 ∈ Grp, 𝑡 ∈ Grp ↦ {𝑔[(Base‘𝑠) / 𝑤](𝑔:𝑤⟶(Base‘𝑡) ∧ ∀𝑥𝑤𝑦𝑤 (𝑔‘(𝑥(+g𝑠)𝑦)) = ((𝑔𝑥)(+g𝑡)(𝑔𝑦)))})
21reldmmpt2 6813 1 Rel dom GrpHom
Colors of variables: wff setvar class
Syntax hints:  wa 383   = wceq 1523  {cab 2637  wral 2941  [wsbc 3468  dom cdm 5143  Rel wrel 5148  wf 5922  cfv 5926  (class class class)co 6690  Basecbs 15904  +gcplusg 15988  Grpcgrp 17469   GrpHom cghm 17704
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1762  ax-4 1777  ax-5 1879  ax-6 1945  ax-7 1981  ax-9 2039  ax-10 2059  ax-11 2074  ax-12 2087  ax-13 2282  ax-ext 2631  ax-sep 4814  ax-nul 4822  ax-pr 4936
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1056  df-tru 1526  df-ex 1745  df-nf 1750  df-sb 1938  df-eu 2502  df-mo 2503  df-clab 2638  df-cleq 2644  df-clel 2647  df-nfc 2782  df-rab 2950  df-v 3233  df-dif 3610  df-un 3612  df-in 3614  df-ss 3621  df-nul 3949  df-if 4120  df-sn 4211  df-pr 4213  df-op 4217  df-br 4686  df-opab 4746  df-xp 5149  df-rel 5150  df-dm 5153  df-oprab 6694  df-mpt2 6695  df-ghm 17705
This theorem is referenced by: (None)
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