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Theorem eximd 1971
Description: Deduction form of Theorem 19.22 of [Margaris] p. 90, see exim 1717. (Contributed by NM, 29-Jun-1993.) (Revised 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 1963 . 2  |-  ( ph  ->  A. x ph )
3 eximd.2 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
42, 3eximdh 1735 1  |-  ( ph  ->  ( E. x ps 
->  E. x ch )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1674   F/wnf 1678
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-12 1944
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1675  df-nf 1679
This theorem is referenced by:  exlimd  2008  19.41  2062  2ax6elem  2289  mopick2  2380  2euex  2384  reximd2a  2869  ssrexf  3504  axpowndlem3  9050  axregndlem1  9053  axregnd  9055  spc2ed  28155  padct  28356  finminlem  31023  bj-mo3OLD  31492  wl-euequ1f  31948  pmapglb2xN  33382  disjinfi  37506  infrpge  37612  fsumiunss  37692  islpcn  37757  stoweidlem27  37925  stoweidlem34  37933  stoweidlem35  37934  sge0rpcpnf  38301
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