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Theorem exdistr2 1850
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 1848 . 2  |-  ( E. y E. z (
ph  /\  ps )  <->  (
ph  /\  E. y E. z ps ) )
21exbii 1569 1  |-  ( E. x E. y E. z ( ph  /\  ps )  <->  E. x ( ph  /\ 
E. y E. z ps ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    /\ wa 358   E.wex 1528
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532
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