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Definition df-iin 3972
 Description: Define indexed intersection. Definition of [Stoll] p. 45. See the remarks for its sibling operation of indexed union df-iun 3971. An alternate definition tying indexed intersection to ordinary intersection is dfiin2 4002. Theorem intiin 4020 provides a definition of ordinary intersection in terms of indexed intersection. (Contributed by NM, 27-Jun-1998.)
Assertion
Ref Expression
df-iin x A B = {y x A y B}
Distinct variable groups:   x,y   y,A   y,B
Allowed substitution hints:   A(x)   B(x)

Detailed syntax breakdown of Definition df-iin
StepHypRef Expression
1 vx . . 3 setvar x
2 cA . . 3 class A
3 cB . . 3 class B
41, 2, 3ciin 3970 . 2 class x A B
5 vy . . . . . 6 setvar y
65cv 1641 . . . . 5 class y
76, 3wcel 1710 . . . 4 wff y B
87, 1, 2wral 2614 . . 3 wff x A y B
98, 5cab 2339 . 2 class {y x A y B}
104, 9wceq 1642 1 wff x A B = {y x A y B}
 Colors of variables: wff setvar class This definition is referenced by:  eliin  3974  iineq1  3983  iineq2  3986  nfiin  3996  nfii1  3998  dfiin2g  4000  cbviin  4004  intiin  4020  0iin  4024  viin  4025  iinxsng  4042
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