Metamath Proof Explorer

Theorem abscld

Description: Real closure of absolute value. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypothesis abscld.1 
|- ( ph -> A e. CC )
Assertion abscld 
|- ( ph -> ( abs ` A ) e. RR )

Proof

Step Hyp Ref Expression
1 abscld.1 
 |-  ( ph -> A e. CC )
2 abscl 
 |-  ( A e. CC -> ( abs ` A ) e. RR )
3 1 2 syl 
 |-  ( ph -> ( abs ` A ) e. RR )