Theorem times2

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

	Ref	Expression
Assertion	times2	⊢ ( 𝐴 ∈ ℂ → ( 𝐴 · 2 ) = ( 𝐴 + 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		2cn	⊢ 2 ∈ ℂ
2		mulcom	⊢ ( ( 𝐴 ∈ ℂ ∧ 2 ∈ ℂ ) → ( 𝐴 · 2 ) = ( 2 · 𝐴 ) )
3	1 2	mpan2	⊢ ( 𝐴 ∈ ℂ → ( 𝐴 · 2 ) = ( 2 · 𝐴 ) )
4		2times	⊢ ( 𝐴 ∈ ℂ → ( 2 · 𝐴 ) = ( 𝐴 + 𝐴 ) )
5	3 4	eqtrd	⊢ ( 𝐴 ∈ ℂ → ( 𝐴 · 2 ) = ( 𝐴 + 𝐴 ) )