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Theorem rlmfn 16294
Description: ringLMod is a function. (Contributed by Stefan O'Rear, 6-Dec-2014.)
Assertion
Ref Expression
rlmfn  |- ringLMod  Fn  _V

Proof of Theorem rlmfn
Dummy variable  a is distinct from all other variables.
StepHypRef Expression
1 fvex 5771 . 2  |-  ( ( subringAlg  `  a ) `  ( Base `  a ) )  e.  _V
2 df-rgmod 16276 . 2  |- ringLMod  =  ( a  e.  _V  |->  ( ( subringAlg  `  a ) `  ( Base `  a )
) )
31, 2fnmpti 5602 1  |- ringLMod  Fn  _V
Colors of variables: wff set class
Syntax hints:   _Vcvv 2962    Fn wfn 5478   ` cfv 5483   Basecbs 13500   subringAlg csra 16271  ringLModcrglmod 16272
This theorem is referenced by:  lidlval  16296  rspval  16297
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-14 1731  ax-6 1746  ax-7 1751  ax-11 1763  ax-12 1953  ax-ext 2423  ax-sep 4355  ax-nul 4363  ax-pr 4432
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 2291  df-mo 2292  df-clab 2429  df-cleq 2435  df-clel 2438  df-nfc 2567  df-ne 2607  df-ral 2716  df-rex 2717  df-rab 2720  df-v 2964  df-sbc 3168  df-dif 3309  df-un 3311  df-in 3313  df-ss 3320  df-nul 3614  df-if 3764  df-sn 3844  df-pr 3845  df-op 3847  df-uni 4040  df-br 4238  df-opab 4292  df-mpt 4293  df-id 4527  df-xp 4913  df-rel 4914  df-cnv 4915  df-co 4916  df-dm 4917  df-iota 5447  df-fun 5485  df-fn 5486  df-fv 5491  df-rgmod 16276
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