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Definition df-vrmd 17381
Description: Define a free monoid over a set 𝑖 of generators, defined as the set of finite strings on 𝐼 with the operation of concatenation. (Contributed by Mario Carneiro, 27-Sep-2015.)
Assertion
Ref Expression
df-vrmd varFMnd = (𝑖 ∈ V ↦ (𝑗𝑖 ↦ ⟨“𝑗”⟩))
Distinct variable group:   𝑖,𝑗

Detailed syntax breakdown of Definition df-vrmd
StepHypRef Expression
1 cvrmd 17379 . 2 class varFMnd
2 vi . . 3 setvar 𝑖
3 cvv 3198 . . 3 class V
4 vj . . . 4 setvar 𝑗
52cv 1481 . . . 4 class 𝑖
64cv 1481 . . . . 5 class 𝑗
76cs1 13289 . . . 4 class ⟨“𝑗”⟩
84, 5, 7cmpt 4727 . . 3 class (𝑗𝑖 ↦ ⟨“𝑗”⟩)
92, 3, 8cmpt 4727 . 2 class (𝑖 ∈ V ↦ (𝑗𝑖 ↦ ⟨“𝑗”⟩))
101, 9wceq 1482 1 wff varFMnd = (𝑖 ∈ V ↦ (𝑗𝑖 ↦ ⟨“𝑗”⟩))
Colors of variables: wff setvar class
This definition is referenced by:  vrmdfval  17387
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