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Theorem eeor 1628
Description: Rearrange existential quantifiers. (Contributed by NM, 8-Aug-1994.)
Hypotheses
Ref Expression
eeor.1  |-  F/ y
ph
eeor.2  |-  F/ x ps
Assertion
Ref Expression
eeor  |-  ( E. x E. y (
ph  \/  ps )  <->  ( E. x ph  \/  E. y ps ) )

Proof of Theorem eeor
StepHypRef Expression
1 eeor.1 . . . 4  |-  F/ y
ph
2119.45 1616 . . 3  |-  ( E. y ( ph  \/  ps )  <->  ( ph  \/  E. y ps ) )
32exbii 1539 . 2  |-  ( E. x E. y (
ph  \/  ps )  <->  E. x ( ph  \/  E. y ps ) )
4 eeor.2 . . . 4  |-  F/ x ps
54nfex 1571 . . 3  |-  F/ x E. y ps
6519.44 1615 . 2  |-  ( E. x ( ph  \/  E. y ps )  <->  ( E. x ph  \/  E. y ps ) )
73, 6bitri 182 1  |-  ( E. x E. y (
ph  \/  ps )  <->  ( E. x ph  \/  E. y ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 103    \/ wo 662   F/wnf 1392   E.wex 1424
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-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-ial 1470
This theorem depends on definitions:  df-bi 115  df-nf 1393
This theorem is referenced by: (None)
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