Definition df-iin 1997

Description: Define indexed intersection. Definition of [Stoll] p. 45. See the remarks for its sibling operation of indexed union df-iun 1996.

Assertion

Ref	Expression
df-iin	⊢ ∩x ∈ A B = {y∣∀x ∈ A y ∈ B}

Distinct variable group(s):   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 1995	. 2 class ∩x ∈ A B
5		vy	. . . . . 6 set y
6	5	cv 1089	. . . . 5 class y
7	6, 3	wcel 1092	. . . 4 wff y ∈ B
8	7, 1, 2	wral 1201	. . 3 wff ∀x ∈ A y ∈ B
9	8, 5	cab 1090	. 2 class {y∣∀x ∈ A y ∈ B}
10	4, 9	wceq 1091	1 wff ∩x ∈ A B = {y∣∀x ∈ A y ∈ B}

This definition is referenced by:  eliin 1999  iineq1 2004  iineq2 2007  hbii1 2013  dfiin2 2015  intiin 2027

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