Theorem numsq

Description: Square commutes with canonical numerator. (Contributed by Stefan O'Rear, 15-Sep-2014)

	Ref	Expression
Assertion	numsq	|- ( A e. QQ -> ( numer ` ( A ^ 2 ) ) = ( ( numer ` A ) ^ 2 ) )

Proof

Step	Hyp	Ref	Expression
1		numdensq	|- ( A e. QQ -> ( ( numer ` ( A ^ 2 ) ) = ( ( numer ` A ) ^ 2 ) /\ ( denom ` ( A ^ 2 ) ) = ( ( denom ` A ) ^ 2 ) ) )
2	1	simpld	|- ( A e. QQ -> ( numer ` ( A ^ 2 ) ) = ( ( numer ` A ) ^ 2 ) )