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Definition df-1st 5767
 Description: Define a function that extracts the first member, or abscissa, of an ordered pair. Theorem op1st 5773 proves that it does this. For example, (1st ‘⟨ 3 , 4 ⟩) = 3 . Equivalent to Definition 5.13 (i) of [Monk1] p. 52 (compare op1sta 4802 and op1stb 4209). 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 5765 . 2 class 1st
2 vx . . 3 setvar 𝑥
3 cvv 2557 . . 3 class V
42cv 1242 . . . . . 6 class 𝑥
54csn 3375 . . . . 5 class {𝑥}
65cdm 4345 . . . 4 class dom {𝑥}
76cuni 3580 . . 3 class dom {𝑥}
82, 3, 7cmpt 3818 . 2 class (𝑥 ∈ V ↦ dom {𝑥})
91, 8wceq 1243 1 wff 1st = (𝑥 ∈ V ↦ dom {𝑥})
 Colors of variables: wff set class This definition is referenced by:  1stvalg  5769  fo1st  5784  f1stres  5786
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