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Theorem pm11.61 31543
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 1955 . 2  |-  ( E. y A. x (
ph  ->  ps )  ->  A. x E. y (
ph  ->  ps ) )
2 19.37v 1773 . . . 4  |-  ( E. y ( ph  ->  ps )  <->  ( ph  ->  E. y ps ) )
32biimpi 194 . . 3  |-  ( E. y ( ph  ->  ps )  ->  ( ph  ->  E. y ps )
)
43alimi 1638 . 2  |-  ( A. x E. y ( ph  ->  ps )  ->  A. x
( ph  ->  E. y ps ) )
51, 4syl 16 1  |-  ( E. y A. x (
ph  ->  ps )  ->  A. x ( ph  ->  E. y ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   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  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859
This theorem depends on definitions:  df-bi 185  df-ex 1618  df-nf 1622
This theorem is referenced by: (None)
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