Metamath Proof Explorer
Description: An equality transitivity equality deduction. (Contributed by NM, 18Jul1995)


Ref 
Expression 

Hypotheses 
eqtr3d.1 
 ( ph > A = B ) 


eqtr3d.2 
 ( ph > A = C ) 

Assertion 
eqtr3d 
 ( ph > B = C ) 
Proof
Step 
Hyp 
Ref 
Expression 
1 

eqtr3d.1 
 ( ph > A = B ) 
2 

eqtr3d.2 
 ( ph > A = C ) 
3 
1

eqcomd 
 ( ph > B = A ) 
4 
3 2

eqtrd 
 ( ph > B = C ) 