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Definition df-1st 5681
Description: Define a function that extracts the first member, or abscissa, of an ordered pair. Theorem op1st 5687 proves that it does this. For example, (1st ‘⟨ 3 , 4 ) = 3 . Equivalent to Definition 5.13 (i) of [Monk1] p. 52 (compare op1sta 4720 and op1stb 4150). 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 5679 . 2 class 1st
2 vx . . 3 setvar x
3 cvv 2529 . . 3 class V
42cv 1225 . . . . . 6 class x
54csn 3342 . . . . 5 class {x}
65cdm 4263 . . . 4 class dom {x}
76cuni 3546 . . 3 class dom {x}
82, 3, 7cmpt 3784 . 2 class (x V ↦ dom {x})
91, 8wceq 1226 1 wff 1st = (x V ↦ dom {x})
Colors of variables: wff set class
This definition is referenced by:  1stvalg  5683  fo1st  5698  f1stres  5700
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