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Theorem 19.42vvv 1952
Description: Theorem 19.42 of [Margaris] p. 90 with 3 quantifiers. (Contributed by NM, 21-Sep-2011.)
Assertion
Ref Expression
19.42vvv  |-  ( E. x E. y E. z ( ph  /\  ps )  <->  ( ph  /\  E. x E. y E. z ps ) )
Distinct variable groups:    ph, x    ph, y    ph, z
Allowed substitution hints:    ps( x, y, z)

Proof of Theorem 19.42vvv
StepHypRef Expression
1 19.42vv 1951 . . 3  |-  ( E. y E. z (
ph  /\  ps )  <->  (
ph  /\  E. y E. z ps ) )
21exbii 1644 . 2  |-  ( E. x E. y E. z ( ph  /\  ps )  <->  E. x ( ph  /\ 
E. y E. z ps ) )
3 19.42v 1949 . 2  |-  ( E. x ( ph  /\  E. y E. z ps )  <->  ( ph  /\  E. x E. y E. z ps ) )
42, 3bitri 249 1  |-  ( E. x E. y E. z ( ph  /\  ps )  <->  ( ph  /\  E. x E. y E. z ps ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    /\ wa 369   E.wex 1596
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-12 1803
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1597  df-nf 1600
This theorem is referenced by:  ceqsex6v  3155
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