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| Description: Define the intersection of two classes. Definition 5.6 of [TakeutiZaring] p. 16. For alternate definitions in terms of class difference, requiring no dummy variables, see dfin2 2234 and dfin4 2238. For intersection defined in terms of union, see dfin3 2237. |
| Ref | Expression |
|---|---|
| df-in |
|
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cA |
. . 3
| |
| 2 | cB |
. . 3
| |
| 3 | 1, 2 | cin 2036 |
. 2
|
| 4 | vx |
. . . . . 6
| |
| 5 | 4 | cv 952 |
. . . . 5
|
| 6 | 5, 1 | wcel 955 |
. . . 4
|
| 7 | 5, 2 | wcel 955 |
. . . 4
|
| 8 | 6, 7 | wa 223 |
. . 3
|
| 9 | 8, 4 | cab 1456 |
. 2
|
| 10 | 3, 9 | wceq 953 |
1
|
| Colors of variables: wff set class |
| This definition is referenced by: dfin5 2042 dfss2 2048 elin 2197 disj 2301 |