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 ∈ V ↦ ∪ 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	⊢ ∪ dom { 𝑥 }
7	1 2 6	cmpt	⊢ ( 𝑥 ∈ V ↦ ∪ dom { 𝑥 } )
8	0 7	wceq	⊢ 1st = ( 𝑥 ∈ V ↦ ∪ dom { 𝑥 } )