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Mirrors > Home > MPE Home > Th. List > df-vr1 | Structured version Visualization version GIF version |
Description: Define the base element of a univariate power series (the 𝑋 element of the set 𝑅[𝑋] of polynomials and also the 𝑋 in the set 𝑅[[𝑋]] of power series). (Contributed by Mario Carneiro, 8-Feb-2015.) |
Ref | Expression |
---|---|
df-vr1 | ⊢ var1 = (𝑟 ∈ V ↦ ((1𝑜 mVar 𝑟)‘∅)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cv1 19546 | . 2 class var1 | |
2 | vr | . . 3 setvar 𝑟 | |
3 | cvv 3200 | . . 3 class V | |
4 | c0 3915 | . . . 4 class ∅ | |
5 | c1o 7553 | . . . . 5 class 1𝑜 | |
6 | 2 | cv 1482 | . . . . 5 class 𝑟 |
7 | cmvr 19352 | . . . . 5 class mVar | |
8 | 5, 6, 7 | co 6650 | . . . 4 class (1𝑜 mVar 𝑟) |
9 | 4, 8 | cfv 5888 | . . 3 class ((1𝑜 mVar 𝑟)‘∅) |
10 | 2, 3, 9 | cmpt 4729 | . 2 class (𝑟 ∈ V ↦ ((1𝑜 mVar 𝑟)‘∅)) |
11 | 1, 10 | wceq 1483 | 1 wff var1 = (𝑟 ∈ V ↦ ((1𝑜 mVar 𝑟)‘∅)) |
Colors of variables: wff setvar class |
This definition is referenced by: vr1val 19562 |
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