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Theorem rlmfn 19965
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 6686 . 2 ((subringAlg ‘𝑎)‘(Base‘𝑎)) ∈ V
2 df-rgmod 19948 . 2 ringLMod = (𝑎 ∈ V ↦ ((subringAlg ‘𝑎)‘(Base‘𝑎)))
31, 2fnmpti 6494 1 ringLMod Fn V
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3497   Fn wfn 6353  cfv 6358  Basecbs 16486  subringAlg csra 19943  ringLModcrglmod 19944
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1969  ax-7 2014  ax-8 2115  ax-9 2123  ax-10 2144  ax-11 2160  ax-12 2176  ax-ext 2796  ax-sep 5206  ax-nul 5213  ax-pr 5333
This theorem depends on definitions:  df-bi 209  df-an 399  df-or 844  df-3an 1085  df-tru 1539  df-ex 1780  df-nf 1784  df-sb 2069  df-mo 2621  df-eu 2653  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2966  df-ral 3146  df-rex 3147  df-rab 3150  df-v 3499  df-sbc 3776  df-dif 3942  df-un 3944  df-in 3946  df-ss 3955  df-nul 4295  df-if 4471  df-sn 4571  df-pr 4573  df-op 4577  df-uni 4842  df-br 5070  df-opab 5132  df-mpt 5150  df-id 5463  df-xp 5564  df-rel 5565  df-cnv 5566  df-co 5567  df-dm 5568  df-iota 6317  df-fun 6360  df-fn 6361  df-fv 6366  df-rgmod 19948
This theorem is referenced by:  lidlval  19967  rspval  19968
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