Definition df-vr1 19551

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.)

Assertion

Ref	Expression
df-vr1	⊢ var1 = (𝑟 ∈ V ↦ ((1𝑜 mVar 𝑟)‘∅))

Detailed syntax breakdown of Definition df-vr1

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)‘∅))

This definition is referenced by:  vr1val  19562