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Theorem 19.8aOLD 1956
Description: Obsolete proof of 19.8a 1955. Obsolete as of 21-Dec-2020. Can be deleted as soon as the question of why "MM-PA> min exlimiiv" does not give 19.8a 1955 is answered. (Contributed by NM, 9-Jan-1993.) Allow a shortening of sp 1957. (Revised by Wolf Lammen, 13-Jan-2018.) (Proof shortened by Wolf Lammen, 8-Dec-2019.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
19.8aOLD  |-  ( ph  ->  E. x ph )

Proof of Theorem 19.8aOLD
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 ax6ev 1815 . 2  |-  E. y 
y  =  x
2 ax12v 1951 . . . . 5  |-  ( x  =  y  ->  ( ph  ->  A. x ( x  =  y  ->  ph )
) )
3 ax6ev 1815 . . . . 5  |-  E. x  x  =  y
4 exim 1714 . . . . 5  |-  ( A. x ( x  =  y  ->  ph )  -> 
( E. x  x  =  y  ->  E. x ph ) )
52, 3, 4syl6mpi 63 . . . 4  |-  ( x  =  y  ->  ( ph  ->  E. x ph )
)
65equcoms 1872 . . 3  |-  ( y  =  x  ->  ( ph  ->  E. x ph )
)
76exlimiv 1784 . 2  |-  ( E. y  y  =  x  ->  ( ph  ->  E. x ph ) )
81, 7ax-mp 5 1  |-  ( ph  ->  E. x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1450   E.wex 1671
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-12 1950
This theorem depends on definitions:  df-bi 190  df-an 378  df-ex 1672
This theorem is referenced by: (None)
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