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Theorem eximd 1750
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
eximd.1  |-  F/ x ph
eximd.2  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
eximd  |-  ( ph  ->  ( E. x ps 
->  E. x ch )
)

Proof of Theorem eximd
StepHypRef Expression
1 eximd.1 . . 3  |-  F/ x ph
21nfri 1742 . 2  |-  ( ph  ->  A. x ph )
3 eximd.2 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
42, 3eximdh 1575 1  |-  ( ph  ->  ( E. x ps 
->  E. x ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1528   F/wnf 1531
This theorem is referenced by:  19.41  1815  exdistrf  1911  sbied  1976  mo  2165  mopick2  2210  2euex  2215  copsexg  4252  ssopab2  4290  axextnd  8213  axpowndlem3  8221  axregndlem1  8224  axregnd  8226  finminlem  25643  ssrexf  27096  stoweidlem27  27188  stoweidlem34  27195  stoweidlem35  27196  pmapglb2xN  29334
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-ex 1529  df-nf 1532
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