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Theorem 19.41vvv 1877
Description: Theorem 19.41 of [Margaris] p. 90 with 3 quantifiers. (Contributed by NM, 30-Apr-1995.)
Assertion
Ref Expression
19.41vvv  |-  ( E. x E. y E. z ( ph  /\  ps )  <->  ( E. x E. y E. z ph  /\ 
ps ) )
Distinct variable groups:    ps, x    ps, y    ps, z
Allowed substitution hints:    ph( x, y, z)

Proof of Theorem 19.41vvv
StepHypRef Expression
1 19.41vv 1876 . . 3  |-  ( E. y E. z (
ph  /\  ps )  <->  ( E. y E. z ph  /\  ps ) )
21exbii 1585 . 2  |-  ( E. x E. y E. z ( ph  /\  ps )  <->  E. x ( E. y E. z ph  /\ 
ps ) )
3 19.41v 1875 . 2  |-  ( E. x ( E. y E. z ph  /\  ps ) 
<->  ( E. x E. y E. z ph  /\  ps ) )
42, 3bitri 183 1  |-  ( E. x E. y E. z ( ph  /\  ps )  <->  ( E. x E. y E. z ph  /\ 
ps ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104   E.wex 1469
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-17 1507  ax-ial 1515
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  19.41vvvv  1878  eloprabga  5862  dftpos3  6163
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