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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hbe1 1471 | . . 3 | |
2 | 1 | hbn 1632 | . 2 |
3 | 19.8a 1569 | . . . 4 | |
4 | 3 | con3i 621 | . . 3 |
5 | orel1 714 | . . . 4 | |
6 | olc 700 | . . . 4 | |
7 | 5, 6 | impbid1 141 | . . 3 |
8 | 4, 7 | syl 14 | . 2 |
9 | 2, 8 | eubidh 2005 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wo 697 wex 1468 weu 1999 |
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 603 ax-in2 604 ax-io 698 ax-5 1423 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-4 1487 ax-17 1506 ax-ial 1514 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-fal 1337 df-eu 2002 |
This theorem is referenced by: reuun2 3359 |
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