MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-se Unicode version

Definition df-se 4353
Description: Define the set-like predicate. (Contributed by Mario Carneiro, 19-Nov-2014.)
Assertion
Ref Expression
df-se  |-  ( R Se  A  <->  A. x  e.  A  { y  e.  A  |  y R x }  e.  _V )
Distinct variable groups:    x, y, R    x, A, y

Detailed syntax breakdown of Definition df-se
StepHypRef Expression
1 cA . . 3  class  A
2 cR . . 3  class  R
31, 2wse 4350 . 2  wff  R Se  A
4 vy . . . . . . 7  set  y
54cv 1622 . . . . . 6  class  y
6 vx . . . . . . 7  set  x
76cv 1622 . . . . . 6  class  x
85, 7, 2wbr 4023 . . . . 5  wff  y R x
98, 4, 1crab 2547 . . . 4  class  { y  e.  A  |  y R x }
10 cvv 2788 . . . 4  class  _V
119, 10wcel 1684 . . 3  wff  { y  e.  A  |  y R x }  e.  _V
1211, 6, 1wral 2543 . 2  wff  A. x  e.  A  { y  e.  A  |  y R x }  e.  _V
133, 12wb 176 1  wff  ( R Se  A  <->  A. x  e.  A  { y  e.  A  |  y R x }  e.  _V )
Colors of variables: wff set class
This definition is referenced by:  seex  4356  exse  4357  sess1  4361  sess2  4362  nfse  4368  epse  4376  seinxp  4756  dfse2  5046  exse2  5047
  Copyright terms: Public domain W3C validator