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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 556 |
. . . 4
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2 | 1 | 2exbii 1553 |
. . 3
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3 | nfv 1476 |
. . . . 5
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4 | reean.1 |
. . . . 5
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5 | 3, 4 | nfan 1512 |
. . . 4
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6 | nfv 1476 |
. . . . 5
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7 | reean.2 |
. . . . 5
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8 | 6, 7 | nfan 1512 |
. . . 4
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9 | 5, 8 | eean 1866 |
. . 3
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10 | 2, 9 | bitri 183 |
. 2
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11 | r2ex 2414 |
. 2
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12 | df-rex 2381 |
. . 3
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13 | df-rex 2381 |
. . 3
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14 | 12, 13 | anbi12i 451 |
. 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-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 |
This theorem depends on definitions: df-bi 116 df-nf 1405 df-sb 1704 df-cleq 2093 df-clel 2096 df-nfc 2229 df-rex 2381 |
This theorem is referenced by: reeanv 2558 |
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