Theorem add1p1

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

	Ref	Expression
Assertion	add1p1	|- ( N e. CC -> ( ( N + 1 ) + 1 ) = ( N + 2 ) )

Proof

Step	Hyp	Ref	Expression
1		id	|- ( N e. CC -> N e. CC )
2		1cnd	|- ( N e. CC -> 1 e. CC )
3	1 2 2	addassd	|- ( N e. CC -> ( ( N + 1 ) + 1 ) = ( N + ( 1 + 1 ) ) )
4		1p1e2	|- ( 1 + 1 ) = 2
5	4	a1i	|- ( N e. CC -> ( 1 + 1 ) = 2 )
6	5	oveq2d	|- ( N e. CC -> ( N + ( 1 + 1 ) ) = ( N + 2 ) )
7	3 6	eqtrd	|- ( N e. CC -> ( ( N + 1 ) + 1 ) = ( N + 2 ) )