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Definition df-gobi 23940
Description: Define the Godel-set of equivalence. Here the arguments  U and  V are also Godel-sets corresponding to smaller formulae. Note that this is a class expression, not a wff. (Contributed by Mario Carneiro, 14-Jul-2013.)
Assertion
Ref Expression
df-gobi  |-  <->g  =  ( u  e.  _V , 
v  e.  _V  |->  ( ( u  ->g  v ) 
/\g  ( v  ->g  u ) ) )
Distinct variable group:    v, u

Detailed syntax breakdown of Definition df-gobi
StepHypRef Expression
1 cgob 23933 . 2  class  <->g
2 vu . . 3  set  u
3 vv . . 3  set  v
4 cvv 2788 . . 3  class  _V
52cv 1622 . . . . 5  class  u
63cv 1622 . . . . 5  class  v
7 cgoi 23931 . . . . 5  class  ->g
85, 6, 7co 5858 . . . 4  class  ( u 
->g  v )
96, 5, 7co 5858 . . . 4  class  ( v 
->g  u )
10 cgoa 23930 . . . 4  class  /\g
118, 9, 10co 5858 . . 3  class  ( ( u  ->g  v )  /\g  ( v  ->g  u ) )
122, 3, 4, 4, 11cmpt2 5860 . 2  class  ( u  e.  _V ,  v  e.  _V  |->  ( ( u  ->g  v )  /\g  ( v  ->g  u ) ) )
131, 12wceq 1623 1  wff  <->g  =  ( u  e.  _V , 
v  e.  _V  |->  ( ( u  ->g  v ) 
/\g  ( v  ->g  u ) ) )
Colors of variables: wff set class
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