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Theorem exdistr2 1805
Description: Distribution of existential quantifiers. (Contributed by NM, 17-Mar-1995.)
Assertion
Ref Expression
exdistr2  |-  ( E. x E. y E. z ( ph  /\  ps )  <->  E. x ( ph  /\ 
E. y E. z ps ) )
Distinct variable groups:    ph, y    ph, z
Allowed substitution hints:    ph( x)    ps( x, y, z)

Proof of Theorem exdistr2
StepHypRef Expression
1 19.42vv 1803 . 2  |-  ( E. y E. z (
ph  /\  ps )  <->  (
ph  /\  E. y E. z ps ) )
21exbii 1690 1  |-  ( E. x E. y E. z ( ph  /\  ps )  <->  E. x ( ph  /\ 
E. y E. z 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: (None)
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