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Theorem 19.43OLD 1596
Description: Obsolete proof of 19.43 1595 as of 3-May-2016. 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 476 . . . . 5  |-  ( -.  ( ph  \/  ps ) 
<->  ( -.  ph  /\  -.  ps ) )
21albii 1556 . . . 4  |-  ( A. x  -.  ( ph  \/  ps )  <->  A. x ( -. 
ph  /\  -.  ps )
)
3 19.26 1583 . . . 4  |-  ( A. x ( -.  ph  /\ 
-.  ps )  <->  ( A. x  -.  ph  /\  A. x  -.  ps ) )
4 alnex 1533 . . . . 5  |-  ( A. x  -.  ph  <->  -.  E. x ph )
5 alnex 1533 . . . . 5  |-  ( A. x  -.  ps  <->  -.  E. x ps )
64, 5anbi12i 678 . . . 4  |-  ( ( A. x  -.  ph  /\ 
A. x  -.  ps ) 
<->  ( -.  E. x ph  /\  -.  E. x ps ) )
72, 3, 63bitri 262 . . 3  |-  ( A. x  -.  ( ph  \/  ps )  <->  ( -.  E. x ph  /\  -.  E. x ps ) )
87notbii 287 . 2  |-  ( -. 
A. x  -.  ( ph  \/  ps )  <->  -.  ( -.  E. x ph  /\  -.  E. x ps )
)
9 df-ex 1532 . 2  |-  ( E. x ( ph  \/  ps )  <->  -.  A. x  -.  ( ph  \/  ps ) )
10 oran 482 . 2  |-  ( ( E. x ph  \/  E. x ps )  <->  -.  ( -.  E. x ph  /\  -.  E. x ps )
)
118, 9, 103bitr4i 268 1  |-  ( E. x ( ph  \/  ps )  <->  ( E. x ph  \/  E. x ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    \/ wo 357    /\ 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-or 359  df-an 360  df-ex 1532
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