MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  19.29r2 Unicode version

Theorem 19.29r2 1597
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 1596 . 2  |-  ( ( E. x E. y ph  /\  A. x A. y ps )  ->  E. x
( E. y ph  /\ 
A. y ps )
)
2 19.29r 1596 . . 3  |-  ( ( E. y ph  /\  A. y ps )  ->  E. y ( ph  /\  ps ) )
32eximi 1574 . 2  |-  ( E. x ( E. y ph  /\  A. y ps )  ->  E. x E. y ( ph  /\  ps ) )
41, 3syl 17 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 6    /\ wa 360   A.wal 1532   E.wex 1537
This theorem is referenced by:  2eu6  2198
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538
  Copyright terms: Public domain W3C validator