ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  2eu2ex Unicode version

Theorem 2eu2ex 2086
Description: Double existential uniqueness. (Contributed by NM, 3-Dec-2001.)
Assertion
Ref Expression
2eu2ex  |-  ( E! x E! y ph  ->  E. x E. y ph )

Proof of Theorem 2eu2ex
StepHypRef Expression
1 euex 2027 . 2  |-  ( E! x E! y ph  ->  E. x E! y
ph )
2 euex 2027 . . 3  |-  ( E! y ph  ->  E. y ph )
32eximi 1579 . 2  |-  ( E. x E! y ph  ->  E. x E. y ph )
41, 3syl 14 1  |-  ( E! x E! y ph  ->  E. x E. y ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1468   E!weu 1997
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-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515
This theorem depends on definitions:  df-bi 116  df-nf 1437  df-sb 1736  df-eu 2000
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator