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 e. RR
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