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Metamath Proof Explorer

Theorem times2

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

		Ref	Expression
	Assertion	times2	$⊢ A \in ℂ \to A \cdot 2 = A + A$

Step	Hyp	Ref	Expression
1		2cn	$⊢ 2 \in ℂ$
2		mulcom	$⊢ (A \in ℂ \land 2 \in ℂ) \to A \cdot 2 = 2 A$
3	1 2	mpan2	$⊢ A \in ℂ \to A \cdot 2 = 2 A$
4		2times	$⊢ A \in ℂ \to 2 A = A + A$
5	3 4	eqtrd	$⊢ A \in ℂ \to A \cdot 2 = A + A$