Theorem rlmfn 21122

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.

Step	Hyp	Ref	Expression
1		fvex 6835	. 2 ⊢ ((subringAlg ‘𝑎)‘(Base‘𝑎)) ∈ V
2		df-rgmod 21106	. 2 ⊢ ringLMod = (𝑎 ∈ V ↦ ((subringAlg ‘𝑎)‘(Base‘𝑎)))
3	1, 2	fnmpti 6624	1 ⊢ ringLMod Fn V

Syntax hints:  Vcvv 3436   Fn wfn 6476  ‘cfv 6481  Basecbs 17117  subringAlg csra 21103  ringLModcrglmod 21104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-10 2144  ax-11 2160  ax-12 2180  ax-ext 2703  ax-sep 5234  ax-nul 5244  ax-pr 5370

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-nf 1785  df-sb 2068  df-mo 2535  df-eu 2564  df-clab 2710  df-cleq 2723  df-clel 2806  df-nfc 2881  df-ne 2929  df-ral 3048  df-rex 3057  df-rab 3396  df-v 3438  df-dif 3905  df-un 3907  df-ss 3919  df-nul 4284  df-if 4476  df-sn 4577  df-pr 4579  df-op 4583  df-uni 4860  df-br 5092  df-opab 5154  df-mpt 5173  df-id 5511  df-xp 5622  df-rel 5623  df-cnv 5624  df-co 5625  df-dm 5626  df-iota 6437  df-fun 6483  df-fn 6484  df-fv 6489  df-rgmod 21106

This theorem is referenced by:  lidlval  21145  rspval  21146