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Theorem clmsca 19092
 Description: A complex module is a left module over a subring of the complexes. (Contributed by Mario Carneiro, 16-Oct-2015.)
Hypotheses
Ref Expression
isclm.f Scalar
isclm.k
Assertion
Ref Expression
clmsca CMod flds

Proof of Theorem clmsca
StepHypRef Expression
1 isclm.f . . 3 Scalar
2 isclm.k . . 3
31, 2isclm 19091 . 2 CMod flds SubRingfld
43simp2bi 974 1 CMod flds
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1653   wcel 1726  cfv 5456  (class class class)co 6083  cbs 13471   ↾s cress 13472  Scalarcsca 13534  SubRingcsubrg 15866  clmod 15952  ℂfldccnfld 16705  CModcclm 19089 This theorem is referenced by:  clm0  19099  clm1  19100  clmadd  19101  clmmul  19102  clmcj  19103  clmsub  19107  clmneg  19108  clmabs  19109 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419  ax-nul 4340 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-eu 2287  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-ne 2603  df-ral 2712  df-rex 2713  df-rab 2716  df-v 2960  df-sbc 3164  df-dif 3325  df-un 3327  df-in 3329  df-ss 3336  df-nul 3631  df-if 3742  df-sn 3822  df-pr 3823  df-op 3825  df-uni 4018  df-br 4215  df-iota 5420  df-fv 5464  df-ov 6086  df-clm 19090
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