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Theorem eximOLD 1634
Description: Obsolete proof of exim 1633 as of 4-Sep-2019. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 4-Jul-2014.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
eximOLD  |-  ( A. x ( ph  ->  ps )  ->  ( E. x ph  ->  E. x ps ) )

Proof of Theorem eximOLD
StepHypRef Expression
1 con3 134 . . . 4  |-  ( (
ph  ->  ps )  -> 
( -.  ps  ->  -. 
ph ) )
21al2imi 1616 . . 3  |-  ( A. x ( ph  ->  ps )  ->  ( A. x  -.  ps  ->  A. x  -.  ph ) )
3 alnex 1598 . . 3  |-  ( A. x  -.  ps  <->  -.  E. x ps )
4 alnex 1598 . . 3  |-  ( A. x  -.  ph  <->  -.  E. x ph )
52, 3, 43imtr3g 269 . 2  |-  ( A. x ( ph  ->  ps )  ->  ( -.  E. x ps  ->  -.  E. x ph ) )
65con4d 105 1  |-  ( A. x ( ph  ->  ps )  ->  ( E. x ph  ->  E. x ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1377   E.wex 1596
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612
This theorem depends on definitions:  df-bi 185  df-ex 1597
This theorem is referenced by: (None)
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