Theorem p1lep2

Description: A real number increasd by 1 is less than or equal to the number increased by 2. (Contributed by Alexander van der Vekens, 17-Sep-2018)

	Ref	Expression
Assertion	p1lep2	$$⊢N\in ℝ\to N+1\le N+2$$

Proof

Step	Hyp	Ref	Expression
1		1red	$$⊢N\in ℝ\to 1\in ℝ$$
2		2re	$$⊢2\in ℝ$$
3	2	a1i	$$⊢N\in ℝ\to 2\in ℝ$$
4		id	$$⊢N\in ℝ\to N\in ℝ$$
5		1le2	$$⊢1\le 2$$
6	5	a1i	$$⊢N\in ℝ\to 1\le 2$$
7	1 3 4 6	leadd2dd	$$⊢N\in ℝ\to N+1\le N+2$$