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Theorem 19.43OLD 1617
Description: Obsolete proof of 19.43 1616 as of 3-May-2017. Leave this in for the example on the mmrecent.html page. (Contributed by NM, 5-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
19.43OLD  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  E. x ps ) )

Proof of Theorem 19.43OLD
StepHypRef Expression
1 ioran 478 . . . . 5  |-  ( -.  ( ph  \/  ps ) 
<->  ( -.  ph  /\  -.  ps ) )
21albii 1576 . . . 4  |-  ( A. x  -.  ( ph  \/  ps )  <->  A. x ( -. 
ph  /\  -.  ps )
)
3 19.26 1604 . . . 4  |-  ( A. x ( -.  ph  /\ 
-.  ps )  <->  ( A. x  -.  ph  /\  A. x  -.  ps ) )
4 alnex 1553 . . . . 5  |-  ( A. x  -.  ph  <->  -.  E. x ph )
5 alnex 1553 . . . . 5  |-  ( A. x  -.  ps  <->  -.  E. x ps )
64, 5anbi12i 680 . . . 4  |-  ( ( A. x  -.  ph  /\ 
A. x  -.  ps ) 
<->  ( -.  E. x ph  /\  -.  E. x ps ) )
72, 3, 63bitri 264 . . 3  |-  ( A. x  -.  ( ph  \/  ps )  <->  ( -.  E. x ph  /\  -.  E. x ps ) )
87notbii 289 . 2  |-  ( -. 
A. x  -.  ( ph  \/  ps )  <->  -.  ( -.  E. x ph  /\  -.  E. x ps )
)
9 df-ex 1552 . 2  |-  ( E. x ( ph  \/  ps )  <->  -.  A. x  -.  ( ph  \/  ps ) )
10 oran 484 . 2  |-  ( ( E. x ph  \/  E. x ps )  <->  -.  ( -.  E. x ph  /\  -.  E. x ps )
)
118, 9, 103bitr4i 270 1  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  E. x ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 178    \/ wo 359    /\ wa 360   A.wal 1550   E.wex 1551
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-ex 1552
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