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Mirrors > Home > MPE Home > Th. List > rlmfn | Structured version Visualization version GIF version |
Description: ringLMod is a function. (Contributed by Stefan O'Rear, 6-Dec-2014.) |
Ref | Expression |
---|---|
rlmfn | ⊢ ringLMod Fn V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fvex 6910 | . 2 ⊢ ((subringAlg ‘𝑎)‘(Base‘𝑎)) ∈ V | |
2 | df-rgmod 21059 | . 2 ⊢ ringLMod = (𝑎 ∈ V ↦ ((subringAlg ‘𝑎)‘(Base‘𝑎))) | |
3 | 1, 2 | fnmpti 6698 | 1 ⊢ ringLMod Fn V |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3471 Fn wfn 6543 ‘cfv 6548 Basecbs 17180 subringAlg csra 21056 ringLModcrglmod 21057 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1790 ax-4 1804 ax-5 1906 ax-6 1964 ax-7 2004 ax-8 2101 ax-9 2109 ax-10 2130 ax-11 2147 ax-12 2167 ax-ext 2699 ax-sep 5299 ax-nul 5306 ax-pr 5429 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 847 df-3an 1087 df-tru 1537 df-fal 1547 df-ex 1775 df-nf 1779 df-sb 2061 df-mo 2530 df-eu 2559 df-clab 2706 df-cleq 2720 df-clel 2806 df-nfc 2881 df-ne 2938 df-ral 3059 df-rex 3068 df-rab 3430 df-v 3473 df-dif 3950 df-un 3952 df-in 3954 df-ss 3964 df-nul 4324 df-if 4530 df-sn 4630 df-pr 4632 df-op 4636 df-uni 4909 df-br 5149 df-opab 5211 df-mpt 5232 df-id 5576 df-xp 5684 df-rel 5685 df-cnv 5686 df-co 5687 df-dm 5688 df-iota 6500 df-fun 6550 df-fn 6551 df-fv 6556 df-rgmod 21059 |
This theorem is referenced by: lidlval 21106 rspval 21107 |
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