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Theorem euor 1968
Description: Introduce a disjunct into a uniqueness quantifier. (Contributed by NM, 21-Oct-2005.)
Hypothesis
Ref Expression
euor.1  |-  ( ph  ->  A. x ph )
Assertion
Ref Expression
euor  |-  ( ( -.  ph  /\  E! x ps )  ->  E! x
( ph  \/  ps ) )

Proof of Theorem euor
StepHypRef Expression
1 euor.1 . . . 4  |-  ( ph  ->  A. x ph )
21hbn 1585 . . 3  |-  ( -. 
ph  ->  A. x  -.  ph )
3 biorf 696 . . 3  |-  ( -. 
ph  ->  ( ps  <->  ( ph  \/  ps ) ) )
42, 3eubidh 1948 . 2  |-  ( -. 
ph  ->  ( E! x ps 
<->  E! x ( ph  \/  ps ) ) )
54biimpa 290 1  |-  ( ( -.  ph  /\  E! x ps )  ->  E! x
( ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 102    \/ wo 662   A.wal 1283   E!weu 1942
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291  df-eu 1945
This theorem is referenced by:  euorv  1969
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