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Theorem reldmghm 16960
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 16959 . 2  |-  GrpHom  =  ( s  e.  Grp , 
t  e.  Grp  |->  { g  |  [. ( Base `  s )  /  w ]. ( g : w --> ( Base `  t
)  /\  A. x  e.  w  A. y  e.  w  ( g `  ( x ( +g  `  s ) y ) )  =  ( ( g `  x ) ( +g  `  t
) ( g `  y ) ) ) } )
21reldmmpt2 6426 1  |-  Rel  dom  GrpHom
Colors of variables: wff setvar class
Syntax hints:    /\ wa 376    = wceq 1452   {cab 2457   A.wral 2756   [.wsbc 3255   dom cdm 4839   Rel wrel 4844   -->wf 5585   ` cfv 5589  (class class class)co 6308   Basecbs 15199   +g cplusg 15268   Grpcgrp 16747    GrpHom cghm 16958
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639
This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-br 4396  df-opab 4455  df-xp 4845  df-rel 4846  df-dm 4849  df-oprab 6312  df-mpt2 6313  df-ghm 16959
This theorem is referenced by: (None)
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