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Theorem exdistr 1882
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 1879 . 2  |-  ( E. y ( ph  /\  ps )  <->  ( ph  /\  E. y ps ) )
21exbii 1585 1  |-  ( E. x E. y (
ph  /\  ps )  <->  E. x ( ph  /\  E. y ps ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104   E.wex 1469
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-17 1507  ax-ial 1515
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  exdistrv  1883  19.42vv  1884  3exdistr  1888  sbel2x  1974  sbexyz  1979  sbccomlem  2986  uniuni  4379  coass  5064  subhalfnqq  7245
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