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 e. _V |-> U. dom { x } )

Detailed syntax breakdown of Definition df-1st

Step	Hyp	Ref	Expression
1		c1st 5765	. 2 class 1st
2		vx	. . 3 setvar x
3		cvv 2557	. . 3 class _V
4	2	cv 1242	. . . . . 6 class x
5	4	csn 3375	. . . . 5 class { x }
6	5	cdm 4345	. . . 4 class dom { x }
7	6	cuni 3580	. . 3 class U. dom { x }
8	2, 3, 7	cmpt 3818	. 2 class ( x e. _V |-> U. dom { x } )
9	1, 8	wceq 1243	1 wff 1st = ( x e. _V |-> U. dom { x } )

This definition is referenced by:  1stvalg  5769  fo1st  5784  f1stres  5786