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Theorem exdistr 1859
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 1858 . 2  |-  ( E. y ( ph  /\  ps )  <->  ( ph  /\  E. y ps ) )
21exbii 1572 1  |-  ( E. x E. y (
ph  /\  ps )  <->  E. x ( ph  /\  E. y ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358   E.wex 1531
This theorem is referenced by:  19.42vv  1860  3exdistr  1863  sbel2x  2077  sbccomlem  3074  uniuni  4543  coass  5207  dfiota3  24533  brimg  24547  bnj986  29302  sbel2xNEW7  29586
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535
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