Users' Mathboxes Mathbox for Rodolfo Medina < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  2r19.29 Unicode version

Theorem 2r19.29 26720
Description: Double the quantifiers of theorem r19.29. (Contributed by Rodolfo Medina, 25-Sep-2010.)
Assertion
Ref Expression
2r19.29  |-  ( ( A. x  e.  A  A. y  e.  B  ph 
/\  E. x  e.  A  E. y  e.  B  ps )  ->  E. x  e.  A  E. y  e.  B  ( ph  /\ 
ps ) )

Proof of Theorem 2r19.29
StepHypRef Expression
1 r19.29 2683 . 2  |-  ( ( A. x  e.  A  A. y  e.  B  ph 
/\  E. x  e.  A  E. y  e.  B  ps )  ->  E. x  e.  A  ( A. y  e.  B  ph  /\  E. y  e.  B  ps ) )
2 r19.29 2683 . . 3  |-  ( ( A. y  e.  B  ph 
/\  E. y  e.  B  ps )  ->  E. y  e.  B  ( ph  /\ 
ps ) )
32reximi 2650 . 2  |-  ( E. x  e.  A  ( A. y  e.  B  ph 
/\  E. y  e.  B  ps )  ->  E. x  e.  A  E. y  e.  B  ( ph  /\ 
ps ) )
41, 3syl 15 1  |-  ( ( A. x  e.  A  A. y  e.  B  ph 
/\  E. x  e.  A  E. y  e.  B  ps )  ->  E. x  e.  A  E. y  e.  B  ( ph  /\ 
ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   A.wral 2543   E.wrex 2544
This theorem is referenced by:  prter2  26749
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-ral 2548  df-rex 2549
  Copyright terms: Public domain W3C validator