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Definition df-2nd 5795
Description: Define a function that extracts the second member, or ordinate, of an ordered pair. Theorem op2nd 5801 proves that it does this. For example,  ( 2nd ` 
<. 3 , 4 
>.) = 4 . Equivalent to Definition 5.13 (ii) of [Monk1] p. 52 (compare op2nda 4832 and op2ndb 4831). The notation is the same as Monk's. (Contributed by NM, 9-Oct-2004.)
Assertion
Ref Expression
df-2nd  |-  2nd  =  ( x  e.  _V  |->  U.
ran  { x } )

Detailed syntax breakdown of Definition df-2nd
StepHypRef Expression
1 c2nd 5793 . 2  class  2nd
2 vx . . 3  setvar  x
3 cvv 2574 . . 3  class  _V
42cv 1258 . . . . . 6  class  x
54csn 3402 . . . . 5  class  { x }
65crn 4373 . . . 4  class  ran  {
x }
76cuni 3607 . . 3  class  U. ran  { x }
82, 3, 7cmpt 3845 . 2  class  ( x  e.  _V  |->  U. ran  { x } )
91, 8wceq 1259 1  wff  2nd  =  ( x  e.  _V  |->  U.
ran  { x } )
Colors of variables: wff set class
This definition is referenced by:  2ndvalg  5797  fo2nd  5812  f2ndres  5814
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