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Theorem 19.8aOLD 1884
Description: Obsolete proof of 19.8a 1883 as of 8-Dec-2019. (Contributed by NM, 9-Jan-1993.) (Revised by Wolf Lammen, 13-Jan-2018.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
19.8aOLD  |-  ( ph  ->  E. x ph )

Proof of Theorem 19.8aOLD
Dummy variable  w is distinct from all other variables.
StepHypRef Expression
1 ax6ev 1775 . 2  |-  E. w  w  =  x
2 ax-5 1727 . . . . 5  |-  ( ph  ->  A. w ph )
3 ax-12 1880 . . . . 5  |-  ( x  =  w  ->  ( A. w ph  ->  A. x
( x  =  w  ->  ph ) ) )
4 ax6ev 1775 . . . . . 6  |-  E. x  x  =  w
5 exim 1677 . . . . . 6  |-  ( A. x ( x  =  w  ->  ph )  -> 
( E. x  x  =  w  ->  E. x ph ) )
64, 5mpi 21 . . . . 5  |-  ( A. x ( x  =  w  ->  ph )  ->  E. x ph )
72, 3, 6syl56 34 . . . 4  |-  ( x  =  w  ->  ( ph  ->  E. x ph )
)
87equcoms 1821 . . 3  |-  ( w  =  x  ->  ( ph  ->  E. x ph )
)
98exlimiv 1745 . 2  |-  ( E. w  w  =  x  ->  ( ph  ->  E. x ph ) )
101, 9ax-mp 5 1  |-  ( ph  ->  E. x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1405   E.wex 1635
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-12 1880
This theorem depends on definitions:  df-bi 187  df-ex 1636
This theorem is referenced by: (None)
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