MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-1st Unicode version

Definition df-1st 6021
Description: Define a function that extracts the first member, or abscissa, of an ordered pair. Theorem op1st 6027 proves that it does this. For example,  ( 1st ` 
<. 3 ,  4
>. )  =  3. Equivalent to Definition 5.13 (i) of [Monk1] p. 52 (compare op1sta 5106 and op1stb 4506). 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 6019 . 2  class  1st
2 vx . . 3  set  x
3 cvv 2740 . . 3  class  _V
42cv 1618 . . . . . 6  class  x
54csn 3581 . . . . 5  class  { x }
65cdm 4626 . . . 4  class  dom  {  x }
76cuni 3768 . . 3  class  U. dom  {  x }
82, 3, 7cmpt 4017 . 2  class  ( x  e.  _V  |->  U. dom  {  x } )
91, 8wceq 1619 1  wff  1st  =  ( x  e.  _V  |->  U.
dom  {  x }
)
Colors of variables: wff set class
This definition is referenced by:  1stval  6023  fo1st  6038  f1stres  6040
  Copyright terms: Public domain W3C validator