Metamath Proof Explorer

Theorem nn0ge0d

Description: A nonnegative integer is greater than or equal to zero. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypothesis nn0red.1 
|- ( ph -> A e. NN0 )
Assertion nn0ge0d 
|- ( ph -> 0 <_ A )

Proof

Step Hyp Ref Expression
1 nn0red.1 
 |-  ( ph -> A e. NN0 )
2 nn0ge0 
 |-  ( A e. NN0 -> 0 <_ A )
3 1 2 syl 
 |-  ( ph -> 0 <_ A )