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Theorem 19.35OLD 1693
Description: Obsolete proof of 19.35 1692 as of 4-Sep-2019. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 27-Jun-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
19.35OLD  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)

Proof of Theorem 19.35OLD
StepHypRef Expression
1 19.26 1685 . . . 4  |-  ( A. x ( ph  /\  -.  ps )  <->  ( A. x ph  /\  A. x  -.  ps ) )
2 annim 423 . . . . 5  |-  ( (
ph  /\  -.  ps )  <->  -.  ( ph  ->  ps ) )
32albii 1645 . . . 4  |-  ( A. x ( ph  /\  -.  ps )  <->  A. x  -.  ( ph  ->  ps ) )
4 alnex 1619 . . . . 5  |-  ( A. x  -.  ps  <->  -.  E. x ps )
54anbi2i 692 . . . 4  |-  ( ( A. x ph  /\  A. x  -.  ps )  <->  ( A. x ph  /\  -.  E. x ps )
)
61, 3, 53bitr3i 275 . . 3  |-  ( A. x  -.  ( ph  ->  ps )  <->  ( A. x ph  /\  -.  E. x ps ) )
7 alnex 1619 . . 3  |-  ( A. x  -.  ( ph  ->  ps )  <->  -.  E. x
( ph  ->  ps )
)
8 annim 423 . . 3  |-  ( ( A. x ph  /\  -.  E. x ps )  <->  -.  ( A. x ph  ->  E. x ps )
)
96, 7, 83bitr3i 275 . 2  |-  ( -. 
E. x ( ph  ->  ps )  <->  -.  ( A. x ph  ->  E. x ps ) )
109con4bii 295 1  |-  ( E. x ( ph  ->  ps )  <->  ( A. x ph  ->  E. x ps )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    <-> wb 184    /\ wa 367   A.wal 1396   E.wex 1617
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1618
This theorem is referenced by: (None)
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