Theorem mpaacl

Description: Minimal polynomial is a polynomial. (Contributed by Stefan O'Rear, 25-Nov-2014)

	Ref	Expression
Assertion	mpaacl	|- ( A e. AA -> ( minPolyAA ` A ) e. ( Poly ` QQ ) )

Proof

Step	Hyp	Ref	Expression
1		mpaalem	|- ( A e. AA -> ( ( minPolyAA ` A ) e. ( Poly ` QQ ) /\ ( ( deg ` ( minPolyAA ` A ) ) = ( degAA ` A ) /\ ( ( minPolyAA ` A ) ` A ) = 0 /\ ( ( coeff ` ( minPolyAA ` A ) ) ` ( degAA ` A ) ) = 1 ) ) )
2	1	simpld	|- ( A e. AA -> ( minPolyAA ` A ) e. ( Poly ` QQ ) )