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Mirrors > Home > ILE Home > Th. List > euor2 | Unicode version |
Description: Introduce or eliminate a disjunct in a uniqueness 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 1384 |
. . 3
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2 | 1 | hbn 1544 |
. 2
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3 | 19.8a 1482 |
. . . 4
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4 | 3 | con3i 562 |
. . 3
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5 | orel1 644 |
. . . 4
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6 | olc 632 |
. . . 4
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7 | 5, 6 | impbid1 130 |
. . 3
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8 | 4, 7 | syl 14 |
. 2
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9 | 2, 8 | eubidh 1906 |
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 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-4 1400 ax-17 1419 ax-ial 1427 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 df-eu 1903 |
This theorem is referenced by: reuun2 3220 |
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