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Theorem 19.29r2 1690
Description: Variation of 19.29r 1689 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 1689 . 2  |-  ( ( E. x E. y ph  /\  A. x A. y ps )  ->  E. x
( E. y ph  /\ 
A. y ps )
)
2 19.29r 1689 . . 3  |-  ( ( E. y ph  /\  A. y ps )  ->  E. y ( ph  /\  ps ) )
32eximi 1661 . 2  |-  ( E. x ( E. y ph  /\  A. y ps )  ->  E. x E. y ( ph  /\  ps ) )
41, 3syl 16 1  |-  ( ( E. x E. y ph  /\  A. x A. y ps )  ->  E. x E. y ( ph  /\  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367   A.wal 1396   E.wex 1617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1618
This theorem is referenced by:  2eu6OLD  2381
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