![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > df-iin | Unicode version |
Description: Define indexed intersection. Definition of [Stoll] p. 45. See the remarks for its sibling operation of indexed union df-iun 3886. An alternate definition tying indexed intersection to ordinary intersection is dfiin2 3919. Theorem intiin 3938 provides a definition of ordinary intersection in terms of indexed intersection. (Contributed by NM, 27-Jun-1998.) |
Ref | Expression |
---|---|
df-iin |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vx |
. . 3
![]() ![]() | |
2 | cA |
. . 3
![]() ![]() | |
3 | cB |
. . 3
![]() ![]() | |
4 | 1, 2, 3 | ciin 3885 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() |
5 | vy |
. . . . . 6
![]() ![]() | |
6 | 5 | cv 1352 |
. . . . 5
![]() ![]() |
7 | 6, 3 | wcel 2148 |
. . . 4
![]() ![]() ![]() ![]() |
8 | 7, 1, 2 | wral 2455 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | 8, 5 | cab 2163 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | 4, 9 | wceq 1353 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
This definition is referenced by: eliin 3889 iineq1 3898 iineq2 3901 nfiinxy 3911 nfiinya 3913 nfii1 3915 dfiin2g 3917 cbviin 3922 intiin 3938 0iin 3942 viin 3943 iinxsng 3957 iinxprg 3958 iinuniss 3966 bdciin 14287 |
Copyright terms: Public domain | W3C validator |