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

Theorem 2eximdv 1875
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 3-Aug-1995.)
Hypothesis
Ref Expression
2alimdv.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
2eximdv  |-  ( ph  ->  ( E. x E. y ps  ->  E. x E. y ch ) )
Distinct variable groups:    ph, x    ph, y
Allowed substitution hints:    ps( x, y)    ch( x, y)

Proof of Theorem 2eximdv
StepHypRef Expression
1 2alimdv.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21eximdv 1873 . 2  |-  ( ph  ->  ( E. y ps 
->  E. y ch )
)
32eximdv 1873 1  |-  ( ph  ->  ( E. x E. y ps  ->  E. x E. y ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1485
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-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-17 1519  ax-ial 1527
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  cgsex2g  2766  cgsex4g  2767  spc2egv  2820  spc3egv  2822  relop  4759  elres  4925  opabbrex  5894  th3q  6614  addnnnq0  7398  mulnnnq0  7399  prmuloc  7515  addsrpr  7694  mulsrpr  7695
  Copyright terms: Public domain W3C validator