Theorem add1p1

Description: Adding two times 1 to a number. (Contributed by AV, 22-Sep-2018)

	Ref	Expression
Assertion	add1p1	⊢ ( 𝑁 ∈ ℂ → ( ( 𝑁 + 1 ) + 1 ) = ( 𝑁 + 2 ) )

Proof

Step	Hyp	Ref	Expression
1		id	⊢ ( 𝑁 ∈ ℂ → 𝑁 ∈ ℂ )
2		1cnd	⊢ ( 𝑁 ∈ ℂ → 1 ∈ ℂ )
3	1 2 2	addassd	⊢ ( 𝑁 ∈ ℂ → ( ( 𝑁 + 1 ) + 1 ) = ( 𝑁 + ( 1 + 1 ) ) )
4		1p1e2	⊢ ( 1 + 1 ) = 2
5	4	a1i	⊢ ( 𝑁 ∈ ℂ → ( 1 + 1 ) = 2 )
6	5	oveq2d	⊢ ( 𝑁 ∈ ℂ → ( 𝑁 + ( 1 + 1 ) ) = ( 𝑁 + 2 ) )
7	3 6	eqtrd	⊢ ( 𝑁 ∈ ℂ → ( ( 𝑁 + 1 ) + 1 ) = ( 𝑁 + 2 ) )