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Definition df-int 4405
Description: Define the intersection of a class. Definition 7.35 of [TakeutiZaring] p. 44. For example, {{1, 3}, {1, 8}} = {1}. Compare this with the intersection of two classes, df-in 3546. (Contributed by NM, 18-Aug-1993.)
Assertion
Ref Expression
df-int 𝐴 = {𝑥 ∣ ∀𝑦(𝑦𝐴𝑥𝑦)}
Distinct variable group:   𝑥,𝑦,𝐴

Detailed syntax breakdown of Definition df-int
StepHypRef Expression
1 cA . . 3 class 𝐴
21cint 4404 . 2 class 𝐴
3 vy . . . . . . 7 setvar 𝑦
43cv 1473 . . . . . 6 class 𝑦
54, 1wcel 1976 . . . . 5 wff 𝑦𝐴
6 vx . . . . . 6 setvar 𝑥
76, 3wel 1977 . . . . 5 wff 𝑥𝑦
85, 7wi 4 . . . 4 wff (𝑦𝐴𝑥𝑦)
98, 3wal 1472 . . 3 wff 𝑦(𝑦𝐴𝑥𝑦)
109, 6cab 2595 . 2 class {𝑥 ∣ ∀𝑦(𝑦𝐴𝑥𝑦)}
112, 10wceq 1474 1 wff 𝐴 = {𝑥 ∣ ∀𝑦(𝑦𝐴𝑥𝑦)}
Colors of variables: wff setvar class
This definition is referenced by:  dfint2  4406  elint  4410  int0OLD  4420  dfiin2g  4483
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