Theorem 0le2

Description: The number 0 is less than or equal to 2. (Contributed by David A. Wheeler, 7-Dec-2018)

	Ref	Expression
Assertion	0le2	⊢ 0 ≤ 2

Proof

Step	Hyp	Ref	Expression
1		0le1	⊢ 0 ≤ 1
2		1re	⊢ 1 ∈ ℝ
3	2 2	addge0i	⊢ ( ( 0 ≤ 1 ∧ 0 ≤ 1 ) → 0 ≤ ( 1 + 1 ) )
4	1 1 3	mp2an	⊢ 0 ≤ ( 1 + 1 )
5		df-2	⊢ 2 = ( 1 + 1 )
6	4 5	breqtrri	⊢ 0 ≤ 2