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Theorem 2eximdv 1610
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 3-Aug-1995.)
Hypothesis
Ref Expression
2alimdv.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
2eximdv  |-  ( ph  ->  ( E. x E. y ps  ->  E. x E. y ch ) )
Distinct variable groups:    ph, x    ph, y
Allowed substitution hints:    ps( x, y)    ch( x, y)

Proof of Theorem 2eximdv
StepHypRef Expression
1 2alimdv.1 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
21eximdv 1608 . 2  |-  ( ph  ->  ( E. y ps 
->  E. y ch )
)
32eximdv 1608 1  |-  ( ph  ->  ( E. x E. y ps  ->  E. x E. y ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   E.wex 1528
This theorem is referenced by:  cgsex2g  2821  cgsex4g  2822  spc2egv  2871  spc3egv  2873  relop  4833  elres  4989  th3q  6763  en3  7091  en4  7092  fundmpss  23526  ssoprab2g  24442  pellexlem5  26329  fnchoice  27111  stoweidlem35  27195  a9e2eq  27606
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
This theorem depends on definitions:  df-bi 177  df-ex 1529
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