ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  19.29r2 Unicode version

Theorem 19.29r2 1586
Description: Variation of Theorem 19.29 of [Margaris] p. 90 with double quantification. (Contributed by NM, 3-Feb-2005.)
Assertion
Ref Expression
19.29r2  |-  ( ( E. x E. y ph  /\  A. x A. y ps )  ->  E. x E. y ( ph  /\  ps ) )

Proof of Theorem 19.29r2
StepHypRef Expression
1 19.29r 1585 . 2  |-  ( ( E. x E. y ph  /\  A. x A. y ps )  ->  E. x
( E. y ph  /\ 
A. y ps )
)
2 19.29r 1585 . . 3  |-  ( ( E. y ph  /\  A. y ps )  ->  E. y ( ph  /\  ps ) )
32eximi 1564 . 2  |-  ( E. x ( E. y ph  /\  A. y ps )  ->  E. x E. y ( ph  /\  ps ) )
41, 3syl 14 1  |-  ( ( E. x E. y ph  /\  A. x A. y ps )  ->  E. x E. y ( ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103   A.wal 1314   E.wex 1453
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 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-ial 1499
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator