Definition df-in 3127

Description: Define the intersection of two classes. Definition 5.6 of [TakeutiZaring] p. 16. Contrast this operation with union ( A u. B ) (df-un 3125) and difference ( A \ B ) (df-dif 3123). (Contributed by NM, 29-Apr-1994.)

Assertion

Ref	Expression
df-in	|- ( A i^i B ) = { x | ( x e. A /\ x e. B ) }

Distinct variable groups:   x, A   x, B

Detailed syntax breakdown of Definition df-in

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cB	. . 3 class B
3	1, 2	cin 3120	. 2 class ( A i^i B )
4		vx	. . . . . 6 setvar x
5	4	cv 1347	. . . . 5 class x
6	5, 1	wcel 2141	. . . 4 wff x e. A
7	5, 2	wcel 2141	. . . 4 wff x e. B
8	6, 7	wa 103	. . 3 wff ( x e. A /\ x e. B )
9	8, 4	cab 2156	. 2 class { x | ( x e. A /\ x e. B ) }
10	3, 9	wceq 1348	1 wff ( A i^i B ) = { x | ( x e. A /\ x e. B ) }

This definition is referenced by:  dfin5  3128  dfss2  3136  elin  3310  disj  3463  iinxprg  3947  bdcin  13898