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Theorem eeor 1826
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 1814 . . 3  |-  ( E. y ( ph  \/  ps )  <->  ( ph  \/  E. y ps ) )
32exbii 1569 . 2  |-  ( E. x E. y (
ph  \/  ps )  <->  E. x ( ph  \/  E. y ps ) )
4 eeor.2 . . . 4  |-  F/ x ps
54nfex 1767 . . 3  |-  F/ x E. y ps
6519.44 1813 . 2  |-  ( E. x ( ph  \/  E. y ps )  <->  ( E. x ph  \/  E. y ps ) )
73, 6bitri 240 1  |-  ( E. x E. y (
ph  \/  ps )  <->  ( E. x ph  \/  E. y ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    \/ wo 357   E.wex 1528   F/wnf 1531
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  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532
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