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Theorem pm11.62 27461
Description: Theorem *11.62 in [WhiteheadRussell] p. 166. Importation combined with the rearrangement with quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
pm11.62  |-  ( A. x A. y ( (
ph  /\  ps )  ->  ch )  <->  A. x
( ph  ->  A. y
( ps  ->  ch ) ) )
Distinct variable group:    ph, y
Allowed substitution hints:    ph( x)    ps( x, y)    ch( x, y)

Proof of Theorem pm11.62
StepHypRef Expression
1 impexp 434 . . . 4  |-  ( ( ( ph  /\  ps )  ->  ch )  <->  ( ph  ->  ( ps  ->  ch ) ) )
21albii 1572 . . 3  |-  ( A. y ( ( ph  /\ 
ps )  ->  ch ) 
<-> 
A. y ( ph  ->  ( ps  ->  ch ) ) )
3 19.21v 1909 . . 3  |-  ( A. y ( ph  ->  ( ps  ->  ch )
)  <->  ( ph  ->  A. y ( ps  ->  ch ) ) )
42, 3bitri 241 . 2  |-  ( A. y ( ( ph  /\ 
ps )  ->  ch ) 
<->  ( ph  ->  A. y
( ps  ->  ch ) ) )
54albii 1572 1  |-  ( A. x A. y ( (
ph  /\  ps )  ->  ch )  <->  A. x
( ph  ->  A. y
( ps  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 177    /\ wa 359   A.wal 1546
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-11 1757
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1548  df-nf 1551
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