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Mirrors > Home > ILE Home > Th. List > intpr | Unicode version |
Description: The intersection of a pair is the intersection of its members. Theorem 71 of [Suppes] p. 42. (Contributed by NM, 14-Oct-1999.) |
Ref | Expression |
---|---|
intpr.1 |
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intpr.2 |
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Ref | Expression |
---|---|
intpr |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 19.26 1458 |
. . . 4
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2 | vex 2692 |
. . . . . . . 8
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3 | 2 | elpr 3553 |
. . . . . . 7
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4 | 3 | imbi1i 237 |
. . . . . 6
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5 | jaob 700 |
. . . . . 6
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6 | 4, 5 | bitri 183 |
. . . . 5
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7 | 6 | albii 1447 |
. . . 4
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8 | intpr.1 |
. . . . . 6
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9 | 8 | clel4 2825 |
. . . . 5
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10 | intpr.2 |
. . . . . 6
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11 | 10 | clel4 2825 |
. . . . 5
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12 | 9, 11 | anbi12i 456 |
. . . 4
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13 | 1, 7, 12 | 3bitr4i 211 |
. . 3
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14 | vex 2692 |
. . . 4
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15 | 14 | elint 3785 |
. . 3
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16 | elin 3264 |
. . 3
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17 | 13, 15, 16 | 3bitr4i 211 |
. 2
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18 | 17 | eqriv 2137 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-v 2691 df-un 3080 df-in 3082 df-sn 3538 df-pr 3539 df-int 3780 |
This theorem is referenced by: intprg 3812 op1stb 4407 onintexmid 4495 |
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