Definition df-1st 5787

Description: Define a function that extracts the first member, or abscissa, of an ordered pair. Theorem op1st 5793 proves that it does this. For example, (1^st ‘⟨ 3 , 4 ⟩) = 3 . Equivalent to Definition 5.13 (i) of [Monk1] p. 52 (compare op1sta 4822 and op1stb 4227). 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

Step	Hyp	Ref	Expression
1		c1st 5785	. 2 class 1st
2		vx	. . 3 setvar 𝑥
3		cvv 2601	. . 3 class V
4	2	cv 1283	. . . . . 6 class 𝑥
5	4	csn 3398	. . . . 5 class {𝑥}
6	5	cdm 4363	. . . 4 class dom {𝑥}
7	6	cuni 3601	. . 3 class ∪ dom {𝑥}
8	2, 3, 7	cmpt 3839	. 2 class (𝑥 ∈ V ↦ ∪ dom {𝑥})
9	1, 8	wceq 1284	1 wff 1st = (𝑥 ∈ V ↦ ∪ dom {𝑥})

This definition is referenced by:  1stvalg  5789  fo1st  5804  f1stres  5806