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Theorem exdistr 1829
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 1828 . 2  |-  ( E. y ( ph  /\  ps )  <->  ( ph  /\  E. y ps ) )
21exbii 1537 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-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
This theorem is referenced by:  19.42vv  1830  3exdistr  1834  sbel2x  1916  sbexyz  1921  sbccomlem  2889  uniuni  4203  coass  4863  subhalfnqq  6655
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