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Theorem reldmghm 15751
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 15750 . 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 6206 1  |-  Rel  dom  GrpHom
Colors of variables: wff setvar class
Syntax hints:    /\ wa 369    = wceq 1369   {cab 2429   A.wral 2720   [.wsbc 3191   dom cdm 4845   Rel wrel 4850   -->wf 5419   ` cfv 5423  (class class class)co 6096   Basecbs 14179   +g cplusg 14243   Grpcgrp 15415    GrpHom cghm 15749
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-9 1760  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2423  ax-sep 4418  ax-nul 4426  ax-pr 4536
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-eu 2257  df-mo 2258  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2573  df-ne 2613  df-ral 2725  df-rex 2726  df-rab 2729  df-v 2979  df-dif 3336  df-un 3338  df-in 3340  df-ss 3347  df-nul 3643  df-if 3797  df-sn 3883  df-pr 3885  df-op 3889  df-br 4298  df-opab 4356  df-xp 4851  df-rel 4852  df-dm 4855  df-oprab 6100  df-mpt2 6101  df-ghm 15750
This theorem is referenced by: (None)
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