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Theorem pm11.61 26758
Description: Theorem *11.61 in [WhiteheadRussell] p. 166. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
pm11.61  |-  ( E. y A. x (
ph  ->  ps )  ->  A. x ( ph  ->  E. y ps ) )
Distinct variable group:    ph, y
Allowed substitution hints:    ph( x)    ps( x, y)

Proof of Theorem pm11.61
StepHypRef Expression
1 19.12 1766 . 2  |-  ( E. y A. x (
ph  ->  ps )  ->  A. x E. y (
ph  ->  ps ) )
2 19.37v 2032 . . . 4  |-  ( E. y ( ph  ->  ps )  <->  ( ph  ->  E. y ps ) )
32biimpi 188 . . 3  |-  ( E. y ( ph  ->  ps )  ->  ( ph  ->  E. y ps )
)
43alimi 1546 . 2  |-  ( A. x E. y ( ph  ->  ps )  ->  A. x
( ph  ->  E. y ps ) )
51, 4syl 17 1  |-  ( E. y A. x (
ph  ->  ps )  ->  A. x ( ph  ->  E. y ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532   E.wex 1537
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-17 1628  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540
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