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Theorem spimev 2103
Description: Distinct-variable version of spime 2100. (Contributed by NM, 10-Jan-1993.)
Hypothesis
Ref Expression
spimev.1  |-  ( x  =  y  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
spimev  |-  ( ph  ->  E. x ps )
Distinct variable group:    ph, x
Allowed substitution hints:    ph( y)    ps( x, y)

Proof of Theorem spimev
StepHypRef Expression
1 nfv 1761 . 2  |-  F/ x ph
2 spimev.1 . 2  |-  ( x  =  y  ->  ( ph  ->  ps ) )
31, 2spime 2100 1  |-  ( ph  ->  E. x ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1663
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-12 1933  ax-13 2091
This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668
This theorem is referenced by:  axsep  4524  dtru  4594  zfpair  4637  fvn0ssdmfun  6013  refimssco  36213  rlimdmafv  38679
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