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Theorem 19.28vv 29785
Description: Theorem *11.47 in [WhiteheadRussell] p. 164. Theorem 19.28 of [Margaris] p. 90 with 2 quantifiers. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
19.28vv  |-  ( A. x A. y ( ps 
/\  ph )  <->  ( ps  /\ 
A. x A. y ph ) )
Distinct variable groups:    ps, x    ps, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem 19.28vv
StepHypRef Expression
1 19.28v 1926 . . 3  |-  ( A. y ( ps  /\  ph )  <->  ( ps  /\  A. y ph ) )
21albii 1611 . 2  |-  ( A. x A. y ( ps 
/\  ph )  <->  A. x
( ps  /\  A. y ph ) )
3 19.28v 1926 . 2  |-  ( A. x ( ps  /\  A. y ph )  <->  ( ps  /\ 
A. x A. y ph ) )
42, 3bitri 249 1  |-  ( A. x A. y ( ps 
/\  ph )  <->  ( ps  /\ 
A. x A. y ph ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369   A.wal 1368
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-12 1794
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591
This theorem is referenced by: (None)
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