Definition df-1st 5126

Description: Define a function that extracts the first member, or abscissa, of an ordered pair. Theorem op1st 5132 proves that it does this. Equivalent to Definition 5.13 (i) of [Monk1] p. 52 (compare op1sta 4476 and op1stb 4003). The notation is the same as Monk's.

Assertion

Ref	Expression
df-1st	|- 1st = {<.x, y>. | y = U.dom { x}}

Distinct variable group:   x,y

Detailed syntax breakdown of Definition df-1st

Step	Hyp	Ref	Expression
1		c1st 5124	. 2 class 1st
2		vy	. . . . 5 set y
3	2	cv 1585	. . . 4 class y
4		vx	. . . . . . . 8 set x
5	4	cv 1585	. . . . . . 7 class x
6	5	csn 3238	. . . . . 6 class {x}
7	6	cdm 4119	. . . . 5 class dom { x}
8	7	cuni 3366	. . . 4 class U.dom { x}
9	3, 8	wceq 1586	. . 3 wff y = U.dom { x}
10	9, 4, 2	copab 3565	. 2 class {<.x, y>. | y = U.dom { x}}
11	1, 10	wceq 1586	1 wff 1st = {<.x, y>. | y = U.dom { x}}

This definition is referenced by:  1stval 5128  fo1st 5138  f1stres 5140

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