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Theorem 19.29x 1589
Description: Variation of Theorem 19.29 of [Margaris] p. 90 with mixed quantification. (Contributed by NM, 11-Feb-2005.)
Assertion
Ref Expression
19.29x  |-  ( ( E. x A. y ph  /\  A. x E. y ps )  ->  E. x E. y ( ph  /\  ps ) )

Proof of Theorem 19.29x
StepHypRef Expression
1 19.29r 1587 . 2  |-  ( ( E. x A. y ph  /\  A. x E. y ps )  ->  E. x
( A. y ph  /\ 
E. y ps )
)
2 19.29 1586 . . 3  |-  ( ( A. y ph  /\  E. y ps )  ->  E. y ( ph  /\  ps ) )
32eximi 1566 . 2  |-  ( E. x ( A. y ph  /\  E. y ps )  ->  E. x E. y ( ph  /\  ps ) )
41, 3syl 15 1  |-  ( ( E. x A. y ph  /\  A. x E. y ps )  ->  E. x E. y ( ph  /\  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358   A.wal 1530   E.wex 1531
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532
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