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Mirrors > Home > MPE Home > Th. List > df-iin | Structured version Unicode version |
Description: Define indexed intersection. Definition of [Stoll] p. 45. See the remarks for its sibling operation of indexed union df-iun 4280. An alternate definition tying indexed intersection to ordinary intersection is dfiin2 4312. Theorem intiin 4331 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 4279 |
. 2
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5 | vy |
. . . . . 6
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6 | 5 | cv 1369 |
. . . . 5
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7 | 6, 3 | wcel 1758 |
. . . 4
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8 | 7, 1, 2 | wral 2798 |
. . 3
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9 | 8, 5 | cab 2439 |
. 2
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10 | 4, 9 | wceq 1370 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: eliin 4283 iineq1 4292 iineq2 4295 nfiin 4306 nfii1 4308 dfiin2g 4310 cbviin 4315 intiin 4331 0iin 4335 viin 4336 iinxsng 4354 iinxprg 4355 iinuni 4361 iineq12f 29124 |
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