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Definition df-rgmod 18942
Description: Every ring can be viewed as a left module over itself. (Contributed by Stefan O'Rear, 6-Dec-2014.)
Assertion
Ref Expression
df-rgmod ringLMod = (𝑤 ∈ V ↦ ((subringAlg ‘𝑤)‘(Base‘𝑤)))

Detailed syntax breakdown of Definition df-rgmod
StepHypRef Expression
1 crglmod 18938 . 2 class ringLMod
2 vw . . 3 setvar 𝑤
3 cvv 3172 . . 3 class V
42cv 1473 . . . . 5 class 𝑤
5 cbs 15643 . . . . 5 class Base
64, 5cfv 5789 . . . 4 class (Base‘𝑤)
7 csra 18937 . . . . 5 class subringAlg
84, 7cfv 5789 . . . 4 class (subringAlg ‘𝑤)
96, 8cfv 5789 . . 3 class ((subringAlg ‘𝑤)‘(Base‘𝑤))
102, 3, 9cmpt 4637 . 2 class (𝑤 ∈ V ↦ ((subringAlg ‘𝑤)‘(Base‘𝑤)))
111, 10wceq 1474 1 wff ringLMod = (𝑤 ∈ V ↦ ((subringAlg ‘𝑤)‘(Base‘𝑤)))
Colors of variables: wff setvar class
This definition is referenced by:  rlmfn  18959  rlmval  18960
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