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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 3659. An alternate definition tying indexed intersection to ordinary intersection is dfiin2 3692. Theorem intiin 3711 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 3658 | . 2 |
5 | vy | . . . . . 6 | |
6 | 5 | cv 1242 | . . . . 5 |
7 | 6, 3 | wcel 1393 | . . . 4 |
8 | 7, 1, 2 | wral 2306 | . . 3 |
9 | 8, 5 | cab 2026 | . 2 |
10 | 4, 9 | wceq 1243 | 1 |
Colors of variables: wff set class |
This definition is referenced by: eliin 3662 iineq1 3671 iineq2 3674 nfiinxy 3684 nfiinya 3686 nfii1 3688 dfiin2g 3690 cbviin 3695 intiin 3711 0iin 3715 viin 3716 iinxsng 3730 iinxprg 3731 iinuniss 3737 bdciin 9999 |
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