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Theorem 19.28vv 26750
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 2028 . . 3  |-  ( A. y ( ps  /\  ph )  <->  ( ps  /\  A. y ph ) )
21albii 1554 . 2  |-  ( A. x A. y ( ps 
/\  ph )  <->  A. x
( ps  /\  A. y ph ) )
3 19.28v 2028 . 2  |-  ( A. x ( ps  /\  A. y ph )  <->  ( ps  /\ 
A. x A. y ph ) )
42, 3bitri 242 1  |-  ( A. x A. y ( ps 
/\  ph )  <->  ( ps  /\ 
A. x A. y ph ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    /\ wa 360   A.wal 1532
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-gen 1536  ax-17 1628  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-nf 1540
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