Theorem psr1crng

Description: The ring of univariate power series is a commutative ring. (Contributed by Mario Carneiro, 8-Feb-2015)

	Ref	Expression
Hypothesis	psr1val.1	|- S = ( PwSer1 ` R )
Assertion	psr1crng	|- ( R e. CRing -> S e. CRing )

Proof

Step	Hyp	Ref	Expression
1		psr1val.1	|- S = ( PwSer1 ` R )
2	1	psr1val	|- S = ( ( 1o ordPwSer R ) ` (/) )
3		1on	|- 1o e. On
4	3	a1i	|- ( R e. CRing -> 1o e. On )
5		id	|- ( R e. CRing -> R e. CRing )
6		0ss	|- (/) C_ ( 1o X. 1o )
7	6	a1i	|- ( R e. CRing -> (/) C_ ( 1o X. 1o ) )
8	2 4 5 7	opsrcrng	|- ( R e. CRing -> S e. CRing )