ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  euorv Unicode version

Theorem euorv 2002
Description: Introduce a disjunct into a unique existential quantifier. (Contributed by NM, 23-Mar-1995.)
Assertion
Ref Expression
euorv  |-  ( ( -.  ph  /\  E! x ps )  ->  E! x
( ph  \/  ps ) )
Distinct variable group:    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem euorv
StepHypRef Expression
1 ax-17 1489 . 2  |-  ( ph  ->  A. x ph )
21euor 2001 1  |-  ( ( -.  ph  /\  E! x ps )  ->  E! x
( ph  \/  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 103    \/ wo 680   E!weu 1975
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681  ax-5 1406  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-4 1470  ax-17 1489  ax-ial 1497
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-fal 1320  df-eu 1978
This theorem is referenced by:  eueq2dc  2828
  Copyright terms: Public domain W3C validator