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Theorem eximd 1937
Description: Deduction form of Theorem 19.22 of [Margaris] p. 90, see exim 1700. (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 1929 . 2  |-  ( ph  ->  A. x ph )
3 eximd.2 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
42, 3eximdh 1718 1  |-  ( ph  ->  ( E. x ps 
->  E. x ch )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   E.wex 1657   F/wnf 1661
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-12 1909
This theorem depends on definitions:  df-bi 188  df-ex 1658  df-nf 1662
This theorem is referenced by:  exlimd  1974  19.41  2028  2ax6elem  2255  mopick2  2346  2euex  2350  reximd2a  2834  ssrexf  3467  axpowndlem3  8975  axregndlem1  8978  axregnd  8980  spc2ed  28048  padct  28257  finminlem  30923  bj-mo3OLD  31358  wl-euequ1f  31810  pmapglb2xN  33249  disjinfi  37372  infrpge  37471  fsumiunss  37538  islpcn  37602  stoweidlem27  37770  stoweidlem34  37778  stoweidlem35  37779  sge0rpcpnf  38114
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