ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-1st Structured version   GIF version

Definition df-1st 5709
Description: Define a function that extracts the first member, or abscissa, of an ordered pair. Theorem op1st 5715 proves that it does this. For example, (1st ‘⟨ 3 , 4 ) = 3 . Equivalent to Definition 5.13 (i) of [Monk1] p. 52 (compare op1sta 4745 and op1stb 4175). The notation is the same as Monk's. (Contributed by NM, 9-Oct-2004.)
Assertion
Ref Expression
df-1st 1st = (x V ↦ dom {x})

Detailed syntax breakdown of Definition df-1st
StepHypRef Expression
1 c1st 5707 . 2 class 1st
2 vx . . 3 setvar x
3 cvv 2551 . . 3 class V
42cv 1241 . . . . . 6 class x
54csn 3367 . . . . 5 class {x}
65cdm 4288 . . . 4 class dom {x}
76cuni 3571 . . 3 class dom {x}
82, 3, 7cmpt 3809 . 2 class (x V ↦ dom {x})
91, 8wceq 1242 1 wff 1st = (x V ↦ dom {x})
Colors of variables: wff set class
This definition is referenced by:  1stvalg  5711  fo1st  5726  f1stres  5728
  Copyright terms: Public domain W3C validator