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Definition df-in 2897
 Description: Define the intersection of two classes. Definition 5.6 of [TakeutiZaring] p. 16. Contrast this operation with union (A ∪ B) (df-un 2895) and difference (A ∖ B) (df-dif 2893). (Contributed by NM, 29-Apr-1994.)
Assertion
Ref Expression
df-in (AB) = {x ∣ (x A x B)}
Distinct variable groups:   x,A   x,B

Detailed syntax breakdown of Definition df-in
StepHypRef Expression
1 cA . . 3 class A
2 cB . . 3 class B
31, 2cin 2889 . 2 class (AB)
4 vx . . . . . 6 setvar x
54cv 1225 . . . . 5 class x
65, 1wcel 1370 . . . 4 wff x A
75, 2wcel 1370 . . . 4 wff x B
86, 7wa 97 . . 3 wff (x A x B)
98, 4cab 2004 . 2 class {x ∣ (x A x B)}
103, 9wceq 1226 1 wff (AB) = {x ∣ (x A x B)}
 Colors of variables: wff set class This definition is referenced by:  dfin5  2898  dfss2  2907  elin  3099  disj  3241  iinxprg  3701  bdcin  7229
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