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Theorem 2exim 27680
Description: Theorem *11.34 in [WhiteheadRussell] p. 162. Theorem 19.22 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
2exim  |-  ( A. x A. y ( ph  ->  ps )  ->  ( E. x E. y ph  ->  E. x E. y ps ) )

Proof of Theorem 2exim
StepHypRef Expression
1 exim 1565 . . 3  |-  ( A. y ( ph  ->  ps )  ->  ( E. y ph  ->  E. y ps ) )
21alimi 1549 . 2  |-  ( A. x A. y ( ph  ->  ps )  ->  A. x
( E. y ph  ->  E. y ps )
)
3 exim 1565 . 2  |-  ( A. x ( E. y ph  ->  E. y ps )  ->  ( E. x E. y ph  ->  E. x E. y ps ) )
42, 3syl 15 1  |-  ( A. x A. y ( ph  ->  ps )  ->  ( E. x E. y ph  ->  E. x E. y ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   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-ex 1532
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