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Theorem eeanv 1849
Description: Rearrange existential quantifiers. (Contributed by NM, 26-Jul-1995.)
Assertion
Ref Expression
eeanv  |-  ( E. x E. y (
ph  /\  ps )  <->  ( E. x ph  /\  E. y ps ) )
Distinct variable groups:    ph, y    ps, x
Allowed substitution hints:    ph( x)    ps( y)

Proof of Theorem eeanv
StepHypRef Expression
1 nfv 1462 . 2  |-  F/ y
ph
2 nfv 1462 . 2  |-  F/ x ps
31, 2eean 1848 1  |-  ( E. x E. y (
ph  /\  ps )  <->  ( E. x ph  /\  E. y ps ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 102    <-> wb 103   E.wex 1422
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by:  eeeanv  1850  ee4anv  1851  2eu4  2035  cgsex2g  2636  cgsex4g  2637  vtocl2  2655  spc2egv  2688  spc2gv  2689  dtruarb  3970  copsex2t  4008  copsex2g  4009  opelopabsb  4023  xpmlem  4774  fununi  4998  imain  5012  brabvv  5582  spc2ed  5885  tfrlem7  5966  ener  6326  domtr  6332  unen  6361  ltexprlemdisj  6858  recexprlemdisj  6882
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