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Theorem morimvOLD 2331
Description: Obsolete proof of morimOLD 2330 as of 22-Dec-2018. (Contributed by NM, 28-Jul-1995.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
morimvOLD  |-  ( E* x ( ph  ->  ps )  ->  ( ph  ->  E* x ps )
)
Distinct variable group:    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem morimvOLD
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 ax-1 6 . . . . . . 7  |-  ( ps 
->  ( ph  ->  ps ) )
21a1i 11 . . . . . 6  |-  ( ph  ->  ( ps  ->  ( ph  ->  ps ) ) )
32imim1d 75 . . . . 5  |-  ( ph  ->  ( ( ( ph  ->  ps )  ->  x  =  y )  -> 
( ps  ->  x  =  y ) ) )
43alimdv 1676 . . . 4  |-  ( ph  ->  ( A. x ( ( ph  ->  ps )  ->  x  =  y )  ->  A. x
( ps  ->  x  =  y ) ) )
54eximdv 1677 . . 3  |-  ( ph  ->  ( E. y A. x ( ( ph  ->  ps )  ->  x  =  y )  ->  E. y A. x ( ps  ->  x  =  y ) ) )
6 nfv 1674 . . . 4  |-  F/ y ( ph  ->  ps )
76mo2 2274 . . 3  |-  ( E* x ( ph  ->  ps )  <->  E. y A. x
( ( ph  ->  ps )  ->  x  =  y ) )
8 nfv 1674 . . . 4  |-  F/ y ps
98mo2 2274 . . 3  |-  ( E* x ps  <->  E. y A. x ( ps  ->  x  =  y ) )
105, 7, 93imtr4g 270 . 2  |-  ( ph  ->  ( E* x (
ph  ->  ps )  ->  E* x ps ) )
1110com12 31 1  |-  ( E* x ( ph  ->  ps )  ->  ( ph  ->  E* x ps )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1368   E.wex 1587   E*wmo 2263
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1588  df-nf 1591  df-eu 2266  df-mo 2267
This theorem is referenced by: (None)
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