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Definition df-vrgp 18832
 Description: Define the canonical injection from the generating set 𝐼 into the base set of the free group. (Contributed by Mario Carneiro, 2-Oct-2015.)
Assertion
Ref Expression
df-vrgp varFGrp = (𝑖 ∈ V ↦ (𝑗𝑖 ↦ [⟨“⟨𝑗, ∅⟩”⟩]( ~FG𝑖)))
Distinct variable group:   𝑖,𝑗

Detailed syntax breakdown of Definition df-vrgp
StepHypRef Expression
1 cvrgp 18829 . 2 class varFGrp
2 vi . . 3 setvar 𝑖
3 cvv 3441 . . 3 class V
4 vj . . . 4 setvar 𝑗
52cv 1537 . . . 4 class 𝑖
64cv 1537 . . . . . . 7 class 𝑗
7 c0 4243 . . . . . . 7 class
86, 7cop 4531 . . . . . 6 class 𝑗, ∅⟩
98cs1 13942 . . . . 5 class ⟨“⟨𝑗, ∅⟩”⟩
10 cefg 18827 . . . . . 6 class ~FG
115, 10cfv 6324 . . . . 5 class ( ~FG𝑖)
129, 11cec 8272 . . . 4 class [⟨“⟨𝑗, ∅⟩”⟩]( ~FG𝑖)
134, 5, 12cmpt 5110 . . 3 class (𝑗𝑖 ↦ [⟨“⟨𝑗, ∅⟩”⟩]( ~FG𝑖))
142, 3, 13cmpt 5110 . 2 class (𝑖 ∈ V ↦ (𝑗𝑖 ↦ [⟨“⟨𝑗, ∅⟩”⟩]( ~FG𝑖)))
151, 14wceq 1538 1 wff varFGrp = (𝑖 ∈ V ↦ (𝑗𝑖 ↦ [⟨“⟨𝑗, ∅⟩”⟩]( ~FG𝑖)))
 Colors of variables: wff setvar class This definition is referenced by:  vrgpfval  18887
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