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Theorem clmgrp 18966
Description: A complex module is an additive group. (Contributed by Mario Carneiro, 16-Oct-2015.)
Assertion
Ref Expression
clmgrp  |-  ( W  e. CMod  ->  W  e.  Grp )

Proof of Theorem clmgrp
StepHypRef Expression
1 clmlmod 18965 . 2  |-  ( W  e. CMod  ->  W  e.  LMod )
2 lmodgrp 15886 . 2  |-  ( W  e.  LMod  ->  W  e. 
Grp )
31, 2syl 16 1  |-  ( W  e. CMod  ->  W  e.  Grp )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1717   Grpcgrp 14614   LModclmod 15879  CModcclm 18960
This theorem is referenced by:  clmmulg  18991
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370  ax-nul 4281
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2244  df-clab 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-ne 2554  df-ral 2656  df-rex 2657  df-rab 2660  df-v 2903  df-sbc 3107  df-dif 3268  df-un 3270  df-in 3272  df-ss 3279  df-nul 3574  df-if 3685  df-sn 3765  df-pr 3766  df-op 3768  df-uni 3960  df-br 4156  df-iota 5360  df-fv 5404  df-ov 6025  df-lmod 15881  df-clm 18961
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