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Mirrors > Home > ILE Home > Th. List > intprg | Unicode version |
Description: The intersection of a pair is the intersection of its members. Closed form of intpr 3811. Theorem 71 of [Suppes] p. 42. (Contributed by FL, 27-Apr-2008.) |
Ref | Expression |
---|---|
intprg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | preq1 3608 |
. . . 4
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2 | 1 | inteqd 3784 |
. . 3
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3 | ineq1 3275 |
. . 3
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4 | 2, 3 | eqeq12d 2155 |
. 2
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5 | preq2 3609 |
. . . 4
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6 | 5 | inteqd 3784 |
. . 3
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7 | ineq2 3276 |
. . 3
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8 | 6, 7 | eqeq12d 2155 |
. 2
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9 | vex 2692 |
. . 3
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10 | vex 2692 |
. . 3
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11 | 9, 10 | intpr 3811 |
. 2
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12 | 4, 8, 11 | vtocl2g 2753 |
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-ral 2422 df-v 2691 df-un 3080 df-in 3082 df-sn 3538 df-pr 3539 df-int 3780 |
This theorem is referenced by: intsng 3813 op1stbg 4408 |
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