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Theorem rlmfn 19011
 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 6113 . 2 ((subringAlg ‘𝑎)‘(Base‘𝑎)) ∈ V
2 df-rgmod 18994 . 2 ringLMod = (𝑎 ∈ V ↦ ((subringAlg ‘𝑎)‘(Base‘𝑎)))
31, 2fnmpti 5935 1 ringLMod Fn V
 Colors of variables: wff setvar class Syntax hints:  Vcvv 3173   Fn wfn 5799  ‘cfv 5804  Basecbs 15695  subringAlg csra 18989  ringLModcrglmod 18990 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-sep 4709  ax-nul 4717  ax-pr 4833 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-eu 2462  df-mo 2463  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ral 2901  df-rex 2902  df-rab 2905  df-v 3175  df-sbc 3403  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-uni 4373  df-br 4584  df-opab 4644  df-mpt 4645  df-id 4953  df-xp 5044  df-rel 5045  df-cnv 5046  df-co 5047  df-dm 5048  df-iota 5768  df-fun 5806  df-fn 5807  df-fv 5812  df-rgmod 18994 This theorem is referenced by:  lidlval  19013  rspval  19014
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