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

Theorem exbidh 1550
Description: Formula-building rule for existential quantifier (deduction form). (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
exbidh.1  |-  ( ph  ->  A. x ph )
exbidh.2  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
exbidh  |-  ( ph  ->  ( E. x ps  <->  E. x ch ) )

Proof of Theorem exbidh
StepHypRef Expression
1 exbidh.1 . . 3  |-  ( ph  ->  A. x ph )
2 exbidh.2 . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
31, 2alrimih 1403 . 2  |-  ( ph  ->  A. x ( ps  <->  ch ) )
4 exbi 1540 . 2  |-  ( A. x ( ps  <->  ch )  ->  ( E. x ps  <->  E. x ch ) )
53, 4syl 14 1  |-  ( ph  ->  ( E. x ps  <->  E. x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 103   A.wal 1287   E.wex 1426
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-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-ial 1472
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  exbid  1552  drex2  1667  drex1  1726  exbidv  1753  mobidh  1982
  Copyright terms: Public domain W3C validator