Metamath Proof Explorer
Description: A deduction from three chained equalities. (Contributed by NM, 4Aug2006)


Ref 
Expression 

Hypotheses 
3eqtr2d.1 
 ( ph > A = B ) 


3eqtr2d.2 
 ( ph > C = B ) 


3eqtr2d.3 
 ( ph > C = D ) 

Assertion 
3eqtr2d 
 ( ph > A = D ) 
Proof
Step 
Hyp 
Ref 
Expression 
1 

3eqtr2d.1 
 ( ph > A = B ) 
2 

3eqtr2d.2 
 ( ph > C = B ) 
3 

3eqtr2d.3 
 ( ph > C = D ) 
4 
1 2

eqtr4d 
 ( ph > A = C ) 
5 
4 3

eqtrd 
 ( ph > A = D ) 