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Mirrors > Home > ILE Home > Th. List > reean | Unicode version |
Description: Rearrange existential quantifiers. (Contributed by NM, 27-Oct-2010.) (Proof shortened by Andrew Salmon, 30-May-2011.) |
Ref | Expression |
---|---|
reean.1 |
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reean.2 |
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Ref | Expression |
---|---|
reean |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | an4 576 |
. . . 4
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2 | 1 | 2exbii 1586 |
. . 3
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3 | nfv 1509 |
. . . . 5
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4 | reean.1 |
. . . . 5
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5 | 3, 4 | nfan 1545 |
. . . 4
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6 | nfv 1509 |
. . . . 5
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7 | reean.2 |
. . . . 5
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8 | 6, 7 | nfan 1545 |
. . . 4
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9 | 5, 8 | eean 1904 |
. . 3
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10 | 2, 9 | bitri 183 |
. 2
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11 | r2ex 2458 |
. 2
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12 | df-rex 2423 |
. . 3
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13 | df-rex 2423 |
. . 3
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14 | 12, 13 | anbi12i 456 |
. 2
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15 | 10, 11, 14 | 3bitr4i 211 |
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-nf 1438 df-sb 1737 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rex 2423 |
This theorem is referenced by: reeanv 2603 |
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