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Theorem eximdv 1808
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 27-Apr-1994.)
Hypothesis
Ref Expression
alimdv.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
eximdv  |-  ( ph  ->  ( E. x ps 
->  E. x ch )
)
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    ch( x)

Proof of Theorem eximdv
StepHypRef Expression
1 ax-17 1464 . 2  |-  ( ph  ->  A. x ph )
2 alimdv.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
31, 2eximdh 1547 1  |-  ( ph  ->  ( E. x ps 
->  E. x ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1426
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-4 1445  ax-17 1464  ax-ial 1472
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  2eximdv  1810  reximdv2  2472  cgsexg  2654  spc3egv  2710  euind  2800  ssel  3017  reupick  3281  reximdva0m  3296  uniss  3669  eusvnfb  4267  coss1  4579  coss2  4580  dmss  4623  dmcosseq  4692  funssres  5042  imain  5082  brprcneu  5282  fv3  5312  dffo4  5431  dffo5  5432  f1eqcocnv  5552  mapsn  6427  dmaddpq  6917  dmmulpq  6918  recexprlemlol  7164  recexprlemupu  7166  ioom  9637
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