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Theorem euor2 2272
Description: Introduce or eliminate a disjunct in a uniqueness quantifier. (Contributed by NM, 21-Oct-2005.) (Proof shortened by Andrew Salmon, 9-Jul-2011.)
Assertion
Ref Expression
euor2

Proof of Theorem euor2
StepHypRef Expression
1 nfe1 1732 . . 3  F/
21nfn 1793 . 2  F/
3 19.8a 1756 . . . 4
43con3i 127 . . 3
5 orel1 371 . . . 4
6 olc 373 . . . 4
75, 6impbid1 194 . . 3
84, 7syl 15 . 2
92, 8eubid 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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