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Definition df-1st 5818
Description: Define a function that extracts the first member, or abscissa, of an ordered pair. Theorem op1st 5824 proves that it does this. For example, ( 1st `  <. 3 , 4  >.) = 3 . Equivalent to Definition 5.13 (i) of [Monk1] p. 52 (compare op1sta 4852 and op1stb 4255). The notation is the same as Monk's. (Contributed by NM, 9-Oct-2004.)
Assertion
Ref Expression
df-1st  |-  1st  =  ( x  e.  _V  |->  U.
dom  { x } )

Detailed syntax breakdown of Definition df-1st
StepHypRef Expression
1 c1st 5816 . 2  class  1st
2 vx . . 3  setvar  x
3 cvv 2610 . . 3  class  _V
42cv 1284 . . . . . 6  class  x
54csn 3416 . . . . 5  class  { x }
65cdm 4391 . . . 4  class  dom  {
x }
76cuni 3621 . . 3  class  U. dom  { x }
82, 3, 7cmpt 3859 . 2  class  ( x  e.  _V  |->  U. dom  { x } )
91, 8wceq 1285 1  wff  1st  =  ( x  e.  _V  |->  U.
dom  { x } )
Colors of variables: wff set class
This definition is referenced by:  1stvalg  5820  fo1st  5835  f1stres  5837
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