Description: Equality deduction for unordered pairs. (Contributed by NM, 19Oct2012)
Ref  Expression  

Hypothesis  preq1d.1   ( ph > A = B ) 

Assertion  preq1d   ( ph > { A , C } = { B , C } ) 
Step  Hyp  Ref  Expression 

1  preq1d.1   ( ph > A = B ) 

2  preq1   ( A = B > { A , C } = { B , C } ) 

3  1 2  syl   ( ph > { A , C } = { B , C } ) 