Definition df-in 3163

Description: Define the intersection of two classes. Definition 5.6 of [TakeutiZaring] p. 16. Contrast this operation with union ( A u. B ) (df-un 3161) and difference ( A \ B ) (df-dif 3159). (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 3156	. 2 class ( A i^i B )
4		vx	. . . . . 6 setvar x
5	4	cv 1363	. . . . 5 class x
6	5, 1	wcel 2167	. . . 4 wff x e. A
7	5, 2	wcel 2167	. . . 4 wff x e. B
8	6, 7	wa 104	. . 3 wff ( x e. A /\ x e. B )
9	8, 4	cab 2182	. 2 class { x | ( x e. A /\ x e. B ) }
10	3, 9	wceq 1364	1 wff ( A i^i B ) = { x | ( x e. A /\ x e. B ) }

This definition is referenced by:  dfin5  3164  ssalel  3172  elin  3347  disj  3500  iinxprg  3992  bdcin  15593