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Mirrors > Home > ILE Home > Th. List > euor2 | Unicode version |
Description: Introduce or eliminate a disjunct in a unique existential quantifier. (Contributed by NM, 21-Oct-2005.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
euor2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbe1 1472 |
. . 3
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2 | 1 | hbn 1633 |
. 2
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3 | 19.8a 1570 |
. . . 4
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4 | 3 | con3i 622 |
. . 3
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5 | orel1 715 |
. . . 4
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6 | olc 701 |
. . . 4
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7 | 5, 6 | impbid1 141 |
. . 3
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8 | 4, 7 | syl 14 |
. 2
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9 | 2, 8 | eubidh 2006 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-4 1488 ax-17 1507 ax-ial 1515 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-fal 1338 df-eu 2003 |
This theorem is referenced by: reuun2 3364 |
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