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Definition df-rest 13327
Description: Function returning the subspace topology induced by the topology  y and the set  x. (Contributed by FL, 20-Sep-2010.) (Revised by Mario Carneiro, 1-May-2015.)
Assertion
Ref Expression
df-rest  |-t  =  ( j  e.  _V ,  x  e. 
_V  |->  ran  ( y  e.  j  |->  ( y  i^i  x ) ) )
Distinct variable group:    x, j, y

Detailed syntax breakdown of Definition df-rest
StepHypRef Expression
1 crest 13325 . 2  classt
2 vj . . 3  set  j
3 vx . . 3  set  x
4 cvv 2788 . . 3  class  _V
5 vy . . . . 5  set  y
62cv 1622 . . . . 5  class  j
75cv 1622 . . . . . 6  class  y
83cv 1622 . . . . . 6  class  x
97, 8cin 3151 . . . . 5  class  ( y  i^i  x )
105, 6, 9cmpt 4077 . . . 4  class  ( y  e.  j  |->  ( y  i^i  x ) )
1110crn 4690 . . 3  class  ran  (
y  e.  j  |->  ( y  i^i  x ) )
122, 3, 4, 4, 11cmpt2 5860 . 2  class  ( j  e.  _V ,  x  e.  _V  |->  ran  ( y  e.  j  |->  ( y  i^i  x ) ) )
131, 12wceq 1623 1  wfft  =  ( j  e.  _V ,  x  e. 
_V  |->  ran  ( y  e.  j  |->  ( y  i^i  x ) ) )
Colors of variables: wff set class
This definition is referenced by:  restfn  13329  restval  13331
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