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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 3680. An alternate definition tying indexed intersection to ordinary intersection is dfiin2 3713. Theorem intiin 3732 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 3679 | . 2 |
5 | vy | . . . . . 6 | |
6 | 5 | cv 1283 | . . . . 5 |
7 | 6, 3 | wcel 1433 | . . . 4 |
8 | 7, 1, 2 | wral 2348 | . . 3 |
9 | 8, 5 | cab 2067 | . 2 |
10 | 4, 9 | wceq 1284 | 1 |
Colors of variables: wff set class |
This definition is referenced by: eliin 3683 iineq1 3692 iineq2 3695 nfiinxy 3705 nfiinya 3707 nfii1 3709 dfiin2g 3711 cbviin 3716 intiin 3732 0iin 3736 viin 3737 iinxsng 3751 iinxprg 3752 iinuniss 3758 bdciin 10670 |
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