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Mirrors > Home > ILE Home > Th. List > rextpg | Unicode version |
Description: Convert a quantification over a triple to a disjunction. (Contributed by Mario Carneiro, 23-Apr-2015.) |
Ref | Expression |
---|---|
ralprg.1 |
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ralprg.2 |
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raltpg.3 |
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Ref | Expression |
---|---|
rextpg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ralprg.1 |
. . . . . 6
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2 | ralprg.2 |
. . . . . 6
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3 | 1, 2 | rexprg 3583 |
. . . . 5
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4 | 3 | orbi1d 781 |
. . . 4
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5 | raltpg.3 |
. . . . . 6
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6 | 5 | rexsng 3572 |
. . . . 5
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7 | 6 | orbi2d 780 |
. . . 4
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8 | 4, 7 | sylan9bb 458 |
. . 3
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9 | 8 | 3impa 1177 |
. 2
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10 | df-tp 3540 |
. . . 4
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11 | 10 | rexeqi 2634 |
. . 3
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12 | rexun 3261 |
. . 3
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13 | 11, 12 | bitri 183 |
. 2
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14 | df-3or 964 |
. 2
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15 | 9, 13, 14 | 3bitr4g 222 |
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-3or 964 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rex 2423 df-v 2691 df-sbc 2914 df-un 3080 df-sn 3538 df-pr 3539 df-tp 3540 |
This theorem is referenced by: rextp 3589 |
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