Metamath Proof Explorer

Theorem absge0d

Description: Absolute value is nonnegative. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypothesis abscld.1 
|- ( ph -> A e. CC )
Assertion absge0d 
|- ( ph -> 0 <_ ( abs ` A ) )

Proof

Step Hyp Ref Expression
1 abscld.1 
 |-  ( ph -> A e. CC )
2 absge0 
 |-  ( A e. CC -> 0 <_ ( abs ` A ) )
3 1 2 syl 
 |-  ( ph -> 0 <_ ( abs ` A ) )