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Mirrors > Home > MPE Home > Th. List > df-iin | Structured version Visualization version Unicode version |
Description: Define indexed intersection. Definition of [Stoll] p. 45. See the remarks for its sibling operation of indexed union df-iun 4294. An alternate definition tying indexed intersection to ordinary intersection is dfiin2 4327. Theorem intiin 4346 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 4293 |
. 2
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5 | vy |
. . . . . 6
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6 | 5 | cv 1454 |
. . . . 5
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7 | 6, 3 | wcel 1898 |
. . . 4
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8 | 7, 1, 2 | wral 2749 |
. . 3
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9 | 8, 5 | cab 2448 |
. 2
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10 | 4, 9 | wceq 1455 |
1
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Colors of variables: wff setvar class |
This definition is referenced by: eliin 4298 iineq1 4307 iineq2 4310 nfiin 4321 nfii1 4323 dfiin2g 4325 cbviin 4330 intiin 4346 0iin 4350 viin 4351 iinxsng 4372 iinxprg 4373 iinuni 4381 iineq12f 32454 |
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