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Theorem euor 2311
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 1958 . . 3  |-  F/ x  -.  ph
3 biorf 406 . . 3  |-  ( -. 
ph  ->  ( ps  <->  ( ph  \/  ps ) ) )
42, 3eubid 2286 . 2  |-  ( -. 
ph  ->  ( E! x ps 
<->  E! x ( ph  \/  ps ) ) )
54biimpa 486 1  |-  ( ( -.  ph  /\  E! x ps )  ->  E! x
( ph  \/  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 369    /\ wa 370   F/wnf 1663   E!weu 2266
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1751  ax-6 1797  ax-7 1841  ax-10 1889  ax-12 1907
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-ex 1660  df-nf 1664  df-eu 2270
This theorem is referenced by:  euorv  2312
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