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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 6677 | . 2 ⊢ ((subringAlg ‘𝑎)‘(Base‘𝑎)) ∈ V | |
2 | df-rgmod 19939 | . 2 ⊢ ringLMod = (𝑎 ∈ V ↦ ((subringAlg ‘𝑎)‘(Base‘𝑎))) | |
3 | 1, 2 | fnmpti 6485 | 1 ⊢ ringLMod Fn V |
Colors of variables: wff setvar class |
Syntax hints: Vcvv 3494 Fn wfn 6344 ‘cfv 6349 Basecbs 16477 subringAlg csra 19934 ringLModcrglmod 19935 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 ax-sep 5195 ax-nul 5202 ax-pr 5321 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-mo 2618 df-eu 2650 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-ral 3143 df-rex 3144 df-rab 3147 df-v 3496 df-sbc 3772 df-dif 3938 df-un 3940 df-in 3942 df-ss 3951 df-nul 4291 df-if 4467 df-sn 4561 df-pr 4563 df-op 4567 df-uni 4832 df-br 5059 df-opab 5121 df-mpt 5139 df-id 5454 df-xp 5555 df-rel 5556 df-cnv 5557 df-co 5558 df-dm 5559 df-iota 6308 df-fun 6351 df-fn 6352 df-fv 6357 df-rgmod 19939 |
This theorem is referenced by: lidlval 19958 rspval 19959 |
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