ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-int GIF version

Definition df-int 3616
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 2924. (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 3615 . 2 class 𝐴
3 vy . . . . . . 7 setvar 𝑦
43cv 1242 . . . . . 6 class 𝑦
54, 1wcel 1393 . . . . 5 wff 𝑦𝐴
6 vx . . . . . 6 setvar 𝑥
76, 3wel 1394 . . . . 5 wff 𝑥𝑦
85, 7wi 4 . . . 4 wff (𝑦𝐴𝑥𝑦)
98, 3wal 1241 . . 3 wff 𝑦(𝑦𝐴𝑥𝑦)
109, 6cab 2026 . 2 class {𝑥 ∣ ∀𝑦(𝑦𝐴𝑥𝑦)}
112, 10wceq 1243 1 wff 𝐴 = {𝑥 ∣ ∀𝑦(𝑦𝐴𝑥𝑦)}
Colors of variables: wff set class
This definition is referenced by:  dfint2  3617  elint  3621  int0  3629  dfiin2g  3690  bdcint  9971  bdcriota  9977
  Copyright terms: Public domain W3C validator