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Definition df-in 2918
Description: Define the intersection of two classes. Definition 5.6 of [TakeutiZaring] p. 16. Contrast this operation with union (AB) (df-un 2916) and difference (AB) (df-dif 2914). (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 2910 . 2 class (AB)
4 vx . . . . . 6 setvar x
54cv 1241 . . . . 5 class x
65, 1wcel 1390 . . . 4 wff x A
75, 2wcel 1390 . . . 4 wff x B
86, 7wa 97 . . 3 wff (x A x B)
98, 4cab 2023 . 2 class {x ∣ (x A x B)}
103, 9wceq 1242 1 wff (AB) = {x ∣ (x A x B)}
Colors of variables: wff set class
This definition is referenced by:  dfin5  2919  dfss2  2928  elin  3120  disj  3262  iinxprg  3722  bdcin  9298
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