Metamath Proof Explorer 
< Previous
Next >
Nearby theorems 

Mirrors > Home > MPE Home > Th. List > dfcdeq  Unicode version 
Description: Define conditional equality. All the notation to the left of the is fake; the parentheses and arrows are all part of the notation, which could equally well be written CondEq. On the right side is the actual implication arrow. The reason for this definition is to "flatten" the structure on the right side (whose tree structure is something like (wi (wceq (cv vx) (cv vy)) wph) ) into just (wcdeq vx vy wph). (Contributed by Mario Carneiro, 11Aug2016.) 
Ref  Expression 

dfcdeq  CondEq 
Step  Hyp  Ref  Expression 

1  wph  . . 3  
2  vx  . . 3  
3  vy  . . 3  
4  1, 2, 3  wcdeq 3101  . 2 CondEq 
5  2, 3  weq 1650  . . 3 
6  5, 1  wi 4  . 2 
7  4, 6  wb 177  1 CondEq 
Colors of variables: wff set class 
This definition is referenced by: cdeqi 3103 cdeqri 3104 
Copyright terms: Public domain  W3C validator 