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Definition df-in 2980
Description: Define the intersection of two classes. Definition 5.6 of [TakeutiZaring] p. 16. Contrast this operation with union (𝐴𝐵) (df-un 2978) and difference (𝐴𝐵) (df-dif 2976). (Contributed by NM, 29-Apr-1994.)
Assertion
Ref Expression
df-in (𝐴𝐵) = {𝑥 ∣ (𝑥𝐴𝑥𝐵)}
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 2973 . 2 class (𝐴𝐵)
4 vx . . . . . 6 setvar 𝑥
54cv 1284 . . . . 5 class 𝑥
65, 1wcel 1434 . . . 4 wff 𝑥𝐴
75, 2wcel 1434 . . . 4 wff 𝑥𝐵
86, 7wa 102 . . 3 wff (𝑥𝐴𝑥𝐵)
98, 4cab 2068 . 2 class {𝑥 ∣ (𝑥𝐴𝑥𝐵)}
103, 9wceq 1285 1 wff (𝐴𝐵) = {𝑥 ∣ (𝑥𝐴𝑥𝐵)}
Colors of variables: wff set class
This definition is referenced by:  dfin5  2981  dfss2  2989  elin  3156  disj  3299  iinxprg  3760  bdcin  10812
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