Definition df-iin 2565

Description: Define indexed intersection. Definition of [Stoll] p. 45. See the remarks for its sibling operation of indexed union df-iun 2564. An alternate definition tying indexed intersection to ordinary intersection is dfiun2 2583. Theorem intiin 2598 provides a definition of ordinary intersection in terms of indexed intersection.

Assertion

Ref	Expression
df-iin	|- |^|_x e. A B = {y | A.x e. A y e. B}

Distinct variable groups:   x,y   y,A   y,B

Detailed syntax breakdown of Definition df-iin

Step	Hyp	Ref	Expression
1		vx	. . 3 set x
2		cA	. . 3 class A
3		cB	. . 3 class B
4	1, 2, 3	ciin 2563	. 2 class |^|_x e. A B
5		vy	. . . . . 6 set y
6	5	cv 954	. . . . 5 class y
7	6, 3	wcel 957	. . . 4 wff y e. B
8	7, 1, 2	wral 1643	. . 3 wff A.x e. A y e. B
9	8, 5	cab 1462	. 2 class {y | A.x e. A y e. B}
10	4, 9	wceq 955	1 wff |^|_x e. A B = {y | A.x e. A y e. B}

This definition is referenced by:  eliin 2567  iineq1 2572  iineq2 2575  hbii1 2581  dfiin2 2584  intiin 2598  0iin 2602  iin0 2736

Copyright terms: Public domain