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Definition df-1st 7128
Description: Define a function that extracts the first member, or abscissa, of an ordered pair. Theorem op1st 7136 proves that it does this. For example, (1st ‘⟨3, 4⟩) = 3. Equivalent to Definition 5.13 (i) of [Monk1] p. 52 (compare op1sta 5586 and op1stb 4911). 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 7126 . 2 class 1st
2 vx . . 3 setvar 𝑥
3 cvv 3190 . . 3 class V
42cv 1479 . . . . . 6 class 𝑥
54csn 4155 . . . . 5 class {𝑥}
65cdm 5084 . . . 4 class dom {𝑥}
76cuni 4409 . . 3 class dom {𝑥}
82, 3, 7cmpt 4683 . 2 class (𝑥 ∈ V ↦ dom {𝑥})
91, 8wceq 1480 1 wff 1st = (𝑥 ∈ V ↦ dom {𝑥})
Colors of variables: wff setvar class
This definition is referenced by:  1stval  7130  fo1st  7148  f1stres  7150
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