Users' Mathboxes Mathbox for Mario Carneiro < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  df-sate Structured version   Unicode version

Definition df-sate 25023
Description: A simplified version of the satisfaction predicate, using the standard membership relation and eliminating the extra variable  n. (Contributed by Mario Carneiro, 14-Jul-2013.)
Assertion
Ref Expression
df-sate  |-  Sat E  =  ( m  e. 
_V ,  u  e. 
_V  |->  ( ( ( m  Sat  (  _E 
i^i  ( m  X.  m ) ) ) `
 om ) `  u ) )
Distinct variable group:    u, m

Detailed syntax breakdown of Definition df-sate
StepHypRef Expression
1 csate 25017 . 2  class  Sat E
2 vm . . 3  set  m
3 vu . . 3  set  u
4 cvv 2948 . . 3  class  _V
53cv 1651 . . . 4  class  u
6 com 4837 . . . . 5  class  om
72cv 1651 . . . . . 6  class  m
8 cep 4484 . . . . . . 7  class  _E
97, 7cxp 4868 . . . . . . 7  class  ( m  X.  m )
108, 9cin 3311 . . . . . 6  class  (  _E 
i^i  ( m  X.  m ) )
11 csat 25015 . . . . . 6  class  Sat
127, 10, 11co 6073 . . . . 5  class  ( m  Sat  (  _E  i^i  ( m  X.  m
) ) )
136, 12cfv 5446 . . . 4  class  ( ( m  Sat  (  _E 
i^i  ( m  X.  m ) ) ) `
 om )
145, 13cfv 5446 . . 3  class  ( ( ( m  Sat  (  _E  i^i  ( m  X.  m ) ) ) `
 om ) `  u )
152, 3, 4, 4, 14cmpt2 6075 . 2  class  ( m  e.  _V ,  u  e.  _V  |->  ( ( ( m  Sat  (  _E 
i^i  ( m  X.  m ) ) ) `
 om ) `  u ) )
161, 15wceq 1652 1  wff  Sat E  =  ( m  e. 
_V ,  u  e. 
_V  |->  ( ( ( m  Sat  (  _E 
i^i  ( m  X.  m ) ) ) `
 om ) `  u ) )
Colors of variables: wff set class
  Copyright terms: Public domain W3C validator