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Metamath Proof Explorer

Definition df-1st

Description: Define a function that extracts the first member, or abscissa, of an ordered pair. Theorem op1st proves that it does this. For example, ( 1st<. 3 , 4 >. ) = 3 . Equivalent to Definition 5.13 (i) of Monk1 p. 52 (compare op1sta and op1stb ). The notation is the same as Monk's. (Contributed by NM, 9-Oct-2004)

		Ref	Expression
	Assertion	df-1st	\|- 1st = ( x e. _V \|-> U. dom { x } )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		c1st	\|- 1st
1		vx	\|- x
2		cvv	\|- _V
3	1	cv	\|- x
4	3	csn	\|- { x }
5	4	cdm	\|- dom { x }
6	5	cuni	\|- U. dom { x }
7	1 2 6	cmpt	\|- ( x e. _V \|-> U. dom { x } )
8	0 7	wceq	\|- 1st = ( x e. _V \|-> U. dom { x } )