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Theorem euor 2332
Description: Introduce a disjunct into a uniqueness quantifier. (Contributed by NM, 21-Oct-2005.)
Hypothesis
Ref Expression
euor.1  |-  F/ x ph
Assertion
Ref Expression
euor  |-  ( ( -.  ph  /\  E! x ps )  ->  E! x
( ph  \/  ps ) )

Proof of Theorem euor
StepHypRef Expression
1 euor.1 . . . 4  |-  F/ x ph
21nfn 1849 . . 3  |-  F/ x  -.  ph
3 biorf 405 . . 3  |-  ( -. 
ph  ->  ( ps  <->  ( ph  \/  ps ) ) )
42, 3eubid 2296 . 2  |-  ( -. 
ph  ->  ( E! x ps 
<->  E! x ( ph  \/  ps ) ) )
54biimpa 484 1  |-  ( ( -.  ph  /\  E! x ps )  ->  E! x
( ph  \/  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 368    /\ wa 369   F/wnf 1599   E!weu 2275
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-12 1803
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-ex 1597  df-nf 1600  df-eu 2279
This theorem is referenced by:  euorv  2333
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