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Mirrors > Home > NFE 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 | nfe1 1732 |
. . 3
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2 | 1 | nfn 1793 |
. 2
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3 | 19.8a 1756 |
. . . 4
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4 | 3 | con3i 127 |
. . 3
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5 | orel1 371 |
. . . 4
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6 | olc 373 |
. . . 4
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7 | 5, 6 | impbid1 194 |
. . 3
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8 | 4, 7 | syl 15 |
. 2
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9 | 2, 8 | eubid 2211 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-11 1746 |
This theorem depends on definitions: df-bi 177 df-or 359 df-tru 1319 df-ex 1542 df-nf 1545 df-eu 2208 |
This theorem is referenced by: reuun2 3539 |
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