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Mirrors > Home > ILE Home > Th. List > elpr2 | Unicode version |
Description: A member of an unordered pair of classes is one or the other of them. Exercise 1 of [TakeutiZaring] p. 15. (Contributed by NM, 14-Oct-2005.) |
Ref | Expression |
---|---|
elpr2.1 |
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elpr2.2 |
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Ref | Expression |
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elpr2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elprg 3552 |
. . 3
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2 | 1 | ibi 175 |
. 2
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3 | elpr2.1 |
. . . . . 6
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4 | eleq1 2203 |
. . . . . 6
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5 | 3, 4 | mpbiri 167 |
. . . . 5
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6 | elpr2.2 |
. . . . . 6
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7 | eleq1 2203 |
. . . . . 6
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8 | 6, 7 | mpbiri 167 |
. . . . 5
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9 | 5, 8 | jaoi 706 |
. . . 4
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10 | elprg 3552 |
. . . 4
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11 | 9, 10 | syl 14 |
. . 3
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12 | 11 | ibir 176 |
. 2
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13 | 2, 12 | impbii 125 |
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-sn 3538 df-pr 3539 |
This theorem is referenced by: elxr 9593 |
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