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Theorem exdistr 1802
Description: Distribution of existential quantifiers. (Contributed by NM, 9-Mar-1995.)
Assertion
Ref Expression
exdistr  |-  ( E. x E. y (
ph  /\  ps )  <->  E. x ( ph  /\  E. y ps ) )
Distinct variable group:    ph, y
Allowed substitution hints:    ph( x)    ps( x, y)

Proof of Theorem exdistr
StepHypRef Expression
1 19.42v 1801 . 2  |-  ( E. y ( ph  /\  ps )  <->  ( ph  /\  E. y ps ) )
21exbii 1690 1  |-  ( E. x E. y (
ph  /\  ps )  <->  E. x ( ph  /\  E. y ps ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 186    /\ wa 369   E.wex 1635
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773
This theorem depends on definitions:  df-bi 187  df-an 371  df-ex 1636
This theorem is referenced by:  19.42vv  1803  3exdistr  1806  sbccomlem  3350  coass  5344  uniuni  6593  eulerpartlemgvv  28834  bnj986  29352  dfiota3  30274  ac6s6f  31876
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