Definition df-1st 4085

Description: Define a function that extracts the first member of an ordered pair. Theorem op1st 4091 proves that it does this. Equivalent to Definition 5.13 (i) of [Monk1] p. 52 (compare op1sta 3454 and op1stb 2919). 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 4083	. 2 class 1st
2		vy	. . . . 5 set y
3	2	cv 957	. . . 4 class y
4		vx	. . . . . . . 8 set x
5	4	cv 957	. . . . . . 7 class x
6	5	csn 2413	. . . . . 6 class {x}
7	6	cdm 3176	. . . . 5 class dom { x}
8	7	cuni 2507	. . . 4 class U.dom { x}
9	3, 8	wceq 958	. . 3 wff y = U.dom { x}
10	9, 4, 2	copab 2671	. 2 class {<.x, y>. | y = U.dom { x}}
11	1, 10	wceq 958	1 wff 1st = {<.x, y>. | y = U.dom { x}}

This definition is referenced by:  1stval 4087  fo1st 4097  f1stres 4099

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