Metamath Proof Explorer


Theorem 0le2OLD

Description: Obsolete version of 0le2 as of 10-Jun-2026. (Contributed by David A. Wheeler, 7-Dec-2018) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion 0le2OLD 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