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Theorem euor 2183
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 1777 . . 3  |-  F/ x  -.  ph
3 biorf 394 . . 3  |-  ( -. 
ph  ->  ( ps  <->  ( ph  \/  ps ) ) )
42, 3eubid 2163 . 2  |-  ( -. 
ph  ->  ( E! x ps 
<->  E! x ( ph  \/  ps ) ) )
54biimpa 470 1  |-  ( ( -.  ph  /\  E! x ps )  ->  E! x
( ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 357    /\ wa 358   F/wnf 1534   E!weu 2156
This theorem is referenced by:  euorv  2184
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-eu 2160
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