Theorem 1p1times

Description: Two times a number. (Contributed by NM, 18-May-1999) (Revised by Mario Carneiro, 27-May-2016)

	Ref	Expression
Assertion	1p1times	⊢ ( 𝐴 ∈ ℂ → ( ( 1 + 1 ) · 𝐴 ) = ( 𝐴 + 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		1cnd	⊢ ( 𝐴 ∈ ℂ → 1 ∈ ℂ )
2		id	⊢ ( 𝐴 ∈ ℂ → 𝐴 ∈ ℂ )
3		mulid2	⊢ ( 𝐴 ∈ ℂ → ( 1 · 𝐴 ) = 𝐴 )
4	3 3	oveq12d	⊢ ( 𝐴 ∈ ℂ → ( ( 1 · 𝐴 ) + ( 1 · 𝐴 ) ) = ( 𝐴 + 𝐴 ) )
5	1 2 1 4	joinlmuladdmuld	⊢ ( 𝐴 ∈ ℂ → ( ( 1 + 1 ) · 𝐴 ) = ( 𝐴 + 𝐴 ) )