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Theorem rlmfn 16226
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 5709 . 2  |-  ( ( subringAlg  `  a ) `  ( Base `  a ) )  e.  _V
2 df-rgmod 16208 . 2  |- ringLMod  =  ( a  e.  _V  |->  ( ( subringAlg  `  a ) `  ( Base `  a )
) )
31, 2fnmpti 5540 1  |- ringLMod  Fn  _V
Colors of variables: wff set class
Syntax hints:   _Vcvv 2924    Fn wfn 5416   ` cfv 5421   Basecbs 13432   subringAlg csra 16203  ringLModcrglmod 16204
This theorem is referenced by:  lidlval  16228  rspval  16229
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2393  ax-sep 4298  ax-nul 4306  ax-pr 4371
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-eu 2266  df-mo 2267  df-clab 2399  df-cleq 2405  df-clel 2408  df-nfc 2537  df-ne 2577  df-ral 2679  df-rex 2680  df-rab 2683  df-v 2926  df-sbc 3130  df-dif 3291  df-un 3293  df-in 3295  df-ss 3302  df-nul 3597  df-if 3708  df-sn 3788  df-pr 3789  df-op 3791  df-uni 3984  df-br 4181  df-opab 4235  df-mpt 4236  df-id 4466  df-xp 4851  df-rel 4852  df-cnv 4853  df-co 4854  df-dm 4855  df-iota 5385  df-fun 5423  df-fn 5424  df-fv 5429  df-rgmod 16208
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