Metamath Proof Explorer


Definition df-vr1

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
Assertion df-vr1
|- var1 = ( r e. _V |-> ( ( 1o mVar r ) ` (/) ) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 cv1
 |-  var1
1 vr
 |-  r
2 cvv
 |-  _V
3 c1o
 |-  1o
4 cmvr
 |-  mVar
5 1 cv
 |-  r
6 3 5 4 co
 |-  ( 1o mVar r )
7 c0
 |-  (/)
8 7 6 cfv
 |-  ( ( 1o mVar r ) ` (/) )
9 1 2 8 cmpt
 |-  ( r e. _V |-> ( ( 1o mVar r ) ` (/) ) )
10 0 9 wceq
 |-  var1 = ( r e. _V |-> ( ( 1o mVar r ) ` (/) ) )