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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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfe1 1732 | . . 3 | |
2 | 1 | nfn 1793 | . 2 |
3 | 19.8a 1756 | . . . 4 | |
4 | 3 | con3i 127 | . . 3 |
5 | orel1 371 | . . . 4 | |
6 | olc 373 | . . . 4 | |
7 | 5, 6 | impbid1 194 | . . 3 |
8 | 4, 7 | syl 15 | . 2 |
9 | 2, 8 | eubid 2211 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wi 4 wb 176 wo 357 wex 1541 weu 2204 |
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 3538 |
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