Theorem times2

Description: A number times 2. (Contributed by NM, 16-Oct-2007)

	Ref	Expression
Assertion	times2	|- ( A e. CC -> ( A x. 2 ) = ( A + A ) )

Proof

Step	Hyp	Ref	Expression
1		2cn	|- 2 e. CC
2		mulcom	|- ( ( A e. CC /\ 2 e. CC ) -> ( A x. 2 ) = ( 2 x. A ) )
3	1 2	mpan2	|- ( A e. CC -> ( A x. 2 ) = ( 2 x. A ) )
4		2times	|- ( A e. CC -> ( 2 x. A ) = ( A + A ) )
5	3 4	eqtrd	|- ( A e. CC -> ( A x. 2 ) = ( A + A ) )