Metamath Proof Explorer


Theorem 0le2

Description: The number 0 is less than or equal to 2. (Contributed by David A. Wheeler, 7-Dec-2018) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026)

Ref Expression
Assertion 0le2
|- 0 <_ 2

Proof

Step Hyp Ref Expression
1 0re
 |-  0 e. RR
2 2re
 |-  2 e. RR
3 2nn
 |-  2 e. NN
4 3 nngt0i
 |-  0 < 2
5 1 2 4 ltleii
 |-  0 <_ 2