Metamath Proof Explorer 
< Previous
Next >
Nearby theorems 

Mirrors > Home > MPE Home > Th. List > dfrq  Unicode version 
Description: Define reciprocal on positive fractions. It means the same thing as one divided by the argument (although we don't define full division since we will never need it). This is a "temporary" set used in the construction of complex numbers dfc 8943, and is intended to be used only by the construction. From Proposition 92.5 of [Gleason] p. 119, who uses an asterisk to denote this unary operation. (Contributed by NM, 6Mar1996.) (New usage is discouraged.) 
Ref  Expression 

dfrq 
Step  Hyp  Ref  Expression 

1  crq 8679  . 2  
2  cmq 8678  . . . 4  
3  2  ccnv 4831  . . 3 
4  c1q 8675  . . . 4  
5  4  csn 3771  . . 3 
6  3, 5  cima 4835  . 2 
7  1, 6  wceq 1649  1 
Colors of variables: wff set class 
This definition is referenced by: recmulnq 8788 dmrecnq 8792 
Copyright terms: Public domain  W3C validator 