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Theorem pm11.62 27608
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 435 . . . 4  |-  ( ( ( ph  /\  ps )  ->  ch )  <->  ( ph  ->  ( ps  ->  ch ) ) )
21albii 1576 . . 3  |-  ( A. y ( ( ph  /\ 
ps )  ->  ch ) 
<-> 
A. y ( ph  ->  ( ps  ->  ch ) ) )
3 19.21v 1916 . . 3  |-  ( A. y ( ph  ->  ( ps  ->  ch )
)  <->  ( ph  ->  A. y ( ps  ->  ch ) ) )
42, 3bitri 242 . 2  |-  ( A. y ( ( ph  /\ 
ps )  ->  ch ) 
<->  ( ph  ->  A. y
( ps  ->  ch ) ) )
54albii 1576 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 178    /\ wa 360   A.wal 1550
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-11 1763
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1552  df-nf 1555
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