Metamath Proof Explorer
Description: A mixed syllogism inference, useful for applying a definition to both
sides of an implication. (Contributed by NM, 3Jan1993)


Ref 
Expression 

Hypotheses 
3imtr4.1 
 ( ph > ps ) 


3imtr4.2 
 ( ch <> ph ) 


3imtr4.3 
 ( th <> ps ) 

Assertion 
3imtr4i 
 ( ch > th ) 
Proof
Step 
Hyp 
Ref 
Expression 
1 

3imtr4.1 
 ( ph > ps ) 
2 

3imtr4.2 
 ( ch <> ph ) 
3 

3imtr4.3 
 ( th <> ps ) 
4 
2 1

sylbi 
 ( ch > ps ) 
5 
4 3

sylibr 
 ( ch > th ) 