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Theorem pm11.52 27688
Description: Theorem *11.52 in [WhiteheadRussell] p. 164. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
pm11.52  |-  ( E. x E. y (
ph  /\  ps )  <->  -. 
A. x A. y
( ph  ->  -.  ps ) )

Proof of Theorem pm11.52
StepHypRef Expression
1 df-an 360 . . 3  |-  ( (
ph  /\  ps )  <->  -.  ( ph  ->  -.  ps ) )
212exbii 1573 . 2  |-  ( E. x E. y (
ph  /\  ps )  <->  E. x E. y  -.  ( ph  ->  -.  ps ) )
3 2nalexn 1563 . 2  |-  ( -. 
A. x A. y
( ph  ->  -.  ps ) 
<->  E. x E. y  -.  ( ph  ->  -.  ps ) )
42, 3bitr4i 243 1  |-  ( E. x E. y (
ph  /\  ps )  <->  -. 
A. x A. y
( ph  ->  -.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 176    /\ wa 358   A.wal 1530   E.wex 1531
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532
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