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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 3888. An alternate definition tying indexed intersection to ordinary intersection is dfiin2 3921. Theorem intiin 3941 provides a definition of ordinary intersection in terms of indexed intersection. (Contributed by NM, 27-Jun-1998.) |
Ref | Expression |
---|---|
df-iin |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vx |
. . 3
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2 | cA |
. . 3
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3 | cB |
. . 3
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4 | 1, 2, 3 | ciin 3887 |
. 2
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5 | vy |
. . . . . 6
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6 | 5 | cv 1352 |
. . . . 5
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7 | 6, 3 | wcel 2148 |
. . . 4
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8 | 7, 1, 2 | wral 2455 |
. . 3
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9 | 8, 5 | cab 2163 |
. 2
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10 | 4, 9 | wceq 1353 |
1
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Colors of variables: wff set class |
This definition is referenced by: eliin 3891 iineq1 3900 iineq2 3903 nfiinxy 3913 nfiinya 3915 nfii1 3917 dfiin2g 3919 cbviin 3924 intiin 3941 0iin 3945 viin 3946 iinxsng 3960 iinxprg 3961 iinuniss 3969 bdciin 14601 |
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