Description: Cancellation law for subtraction. (Contributed by Mario Carneiro, 27May2016)
Ref  Expression  

Hypotheses  negidd.1   ( ph > A e. CC ) 

pncand.2   ( ph > B e. CC ) 

Assertion  pncand   ( ph > ( ( A + B )  B ) = A ) 
Step  Hyp  Ref  Expression 

1  negidd.1   ( ph > A e. CC ) 

2  pncand.2   ( ph > B e. CC ) 

3  pncan   ( ( A e. CC /\ B e. CC ) > ( ( A + B )  B ) = A ) 

4  1 2 3  syl2anc   ( ph > ( ( A + B )  B ) = A ) 