Definition df-1st 6374

Description: Define a function that extracts the first member, or abscissa, of an ordered pair. Theorem op1st 6380 proves that it does this. For example, (1^st ‘⟨ 3 , 4 ⟩) = 3 . Equivalent to Definition 5.13 (i) of [Monk1] p. 52 (compare op1sta 5269 and op1stb 4624). 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 6372	. 2 class 1st
2		vx	. . 3 setvar 𝑥
3		cvv 2821	. . 3 class V
4	2	cv 1401	. . . . . 6 class 𝑥
5	4	csn 3709	. . . . 5 class {𝑥}
6	5	cdm 4774	. . . 4 class dom {𝑥}
7	6	cuni 3935	. . 3 class ∪ dom {𝑥}
8	2, 3, 7	cmpt 4192	. 2 class (𝑥 ∈ V ↦ ∪ dom {𝑥})
9	1, 8	wceq 1402	1 wff 1st = (𝑥 ∈ V ↦ ∪ dom {𝑥})

This definition is used by:  1stvalg  6376  fo1st  6391  f1stres  6393